Part 1: Career similarities
There are many similarities between the two. Although he isn't exactly remembered for this, Eisenhower was intelligent and capable. He was a great writer and talented staff member in addition to quickly building himself a reputation as an outstanding teacher for soldiers. His stint as head of Columbia University after World War II was not entirely inconsistent with his army career. Eisenhower wasn't really known as a commander in the field, but rather was more of a desk jockey, until he was appointed to impressive commands by men who had worked with him and appreciated his innate abilities.
Eisenhower also had moments when his judgement was questioned and when he felt he might be relieved of command. The most notable of these came when he chose a controversial general for the North Africa campaign and the French complained loudly only to be overridden by other Ally leaders. British General Montgomery was constantly vocal in his questioning of Eisenhower's decisions. All this is similar to General Clark's background.
Part 2: This is not your Eisenhower's European command
One place where their careers diverge slightly is in being head of NATO and commander of European forces. During Ike's time at the helm it was almost solely a Cold War military operation. Many people still see NATO as merely a remnant of the Cold War but with the fall of the Soviet Union the role of NATO has changed drastically. Unlike General Clark, Ike didn't spend much time working on health care for soldiers and their families or schools for military brats or even on nation-building. General Marshall was responsible for a great deal of nation-building in the years following World War II but Eisenhower mostly worked the military piece of NATO.
In an important contrast, When General Clark was Supreme Allied Commander of Europe, he also had other demands to be met. The role of General Clark, who was both SACEUR and European CinC, was that of military commander and erstwhile regional diplomatic representative of the US. The geographic scope of General Clark's responsibility, from a review of The Mission by Dana Priest:
http://www.prospect.org/print/V14/9/kotkin-s.html
..."Europe"(the realm of the European CinC) stretches in a vast arc from the South African Cape to the Russian Far East.
Priest also discusses how the shift in responsibility came about:
http://flakmag.com/books/themission.html
It's Priest's thesis in a nutshell: In the wake of declining State Department funding and in the face of increased international peacekeeping duties, the American military has evolved into a guiding force, rather than simply a tool, of our country's foreign policy. At the same time this role, because it has evolved so gradually, is surprisingly under-appreciated by the civilian government.
http://www.state.gov/s/p/of/proc/tr/3719.htm
The reality is, under Clinton's watch, the military came to outrank its civilian chain of command in influence, authority, and resources in many parts of the world. How did this come about? The Clinton administration's poor relations with congressional Republicans, especially in the area of foreign policy, led the White House to drop contentious fights over State Department funding and international diplomatic initiatives. They knew that they would get little resistance, however, from Defense committees.
Finally, Priest also gives some examples of what the CinCs have done and can do, with specific examples from General Clark's CinCdom of Kosovo and Africa:
http://www.state.gov/s/p/of/proc/tr/3719.htm
As an institution, the military remains conflicted about such quasi-diplomatic missions as peacekeeping and nation-building. But it has tried to adapt despite itself. Some examples: the CINCs created regional study institutes, joint assignments became prerequisite for promotion, and the Joint Staff grew in skill and numbers, as did the number of military assignments on Capitol Hill, the State Department, and the NSC. The military, as I see it, has been the one to step into a growing gulf between America's unprecedented new leadership role in the world and what America's diplomatic and economic institutions are able to do to fill it. I realized this after traveling the world with all four of the CINCs and after listening to Ambassadors in every one of the 24 countries that I visited with them.
http://flakmag.com/books/themission.html
In dissecting the ways the military has grown into its role, Priest singles out the military's regional command structure as the new front lines of American foreign policy: four military leaders, each overseeing all operations within a given part of the globe, whose unmatched resources and free rein make them virtually modern-day proconsuls (the four foreign commands are Southern, European, Central and Pacific).
Each commander-in-chief (or CinC) has at his disposal an enormous planning budget, a staff of thousands, a personal jet and the ability to dispense humanitarian aid, Special Forces training units and military equipment to American allies.
http://www.manilatimes.net/national/2003/apr/07/opinion/20030407opi3.html
The new nation builders are not just the top guns. Priest found diplomacy/politics is a second language for many globetrotting soldiers of all ranks. Besides fighting and defending, they're expected to be social workers and civic activists resolving conundrums and emergencies formerly handled by civilians. Priest provides numerous examples of officers and grunts performing nonmilitary tasks for which they aren't trained or qualified. In Africa, tough Special Forces sergeants get enmeshed with local religious and tribal issues.
In Kosovo, a lieutenant chose the phone company's board of directors while another young officer, a recent law school graduate, wrote procedures for, then conducted, the country's first postwar criminal hearing. Many, like a frustrated US Army major working in Nigeria, don't like it. "This is what we do," he moans. "We spend most of our time accomplishing foreign policy objectives."
Part 3: Poltical Climate similarities and differences
Perhaps the most interesting similarity is in the non-partisan nature of both prior to entering politics. Regarding Eisenhower:
http://gi.grolier.com/presidents/ea/bios/34peise.html
Prominent DEMOCRATS had tried unsuccessfully to draft Eisenhower for the presidency in 1948. After he became NATO commander, representatives of both parties continued to query him about his availability for 1952. Their interest was due to his widespread popularity and aloofness from partisan strife. Eisenhower was reluctant to enter politics unless he was drafted.
Eisenhower seems to have been a Republican at heart however. From the same source:
The Democrats could have met his conditions and given him a virtually uncontested nomination. Yet he chose to declare that he was a REPUBLICAN because he believed that Democratic policies were promoting centralized government at the expense of individual liberty.
Eisenhower was challenged for the nomination by another Republican. Again from grolier:
However, Sen. Robert A. Taft of Ohio cherished the same conviction and believed that he had a better claim on the Republican presidential nomination.
The Taft faction was largely anti-Truman and believed that Republicans had been losing because they hadn't stood up to Democrats on the issues:
Taft headed a Midwestern faction strongly represented in CONGRESS. It opposed lavish welfare programs at home. It was generally for retrenchment of American commitments abroad and critical of the Truman administration for aiding Europe at the expense of Asia. Although strongly nationalistic, the Taft faction preferred to fight communism by weeding out American subversives than by containment overseas. So it supported the demagogic investigations of Joseph R. McCarthy of Wisconsin, a Republican. In short, it wanted to make an all-out fight on President Truman's Fair Deal and believed that the Republicans had lost the last three presidential ELECTIONS by soft-pedaling major issues.
Moderate Republicans backed General Eisenhower and convinced him to leave his position in Europe and come home and make a successful eleventh hour challenge to the Taft faction:
Eisenhower preferred not to become a factional candidate, but the moderate Eastern wing of the party headed by Gov. Thomas E. Dewey of New York and Sen. Henry Cabot Lodge, Jr., of Massachusetts persuaded him to announce his availability for the nomination. It soon became apparent that the Taft forces were strong enough to prevent a draft. So Eisenhower resigned as supreme commander and returned to the United States on June 1, 1952, to wage a hectic five-week pre-convention campaign.
A major factor General Eisenhower's success was that he seemed more likely to win against the Democrats:
The Taft and Eisenhower forces were so evenly matched that the outcome depended on the decision of some 300 delegates pledged to favorite-son candidates. In the end, they coalesced behind Eisenhower, and helped unseat contested Taft delegates from three Southern states. Eisenhower was nominated by a narrow margin on the first ballot. A number of delegates who voted for him would have preferred Taft but did not think the latter could win in November. The same reasoning led them to support a moderate platform.