While the Israeli Defense forces clearly outclass their immediate neighbors in miltary strength by an order of magnitude or more, their ability to cope with Turkey in an armed confrontation is far less certain.
Since Israel's war for independence its armed forces have been hardened in the crucible of combat and achieved such dominance over its immediate neighbors that none of them have been willing to challenge the IDF in conventional combat for a generation. Instead Israel's opponents have engaged in a protracted struggle using unconventional means including terrorism. This long war may have dulled the Israelis competence in conventional warfare and it definitely seems to have blinded them to the potential consequences of taking on a major military power like Turkey.
Israel's first line of defense is its air force, which reportedly has around 368 first-line combat aircraft, mostly F-16s and F-15s. Turkey, however, has a similar force of more than 400 combat aircraft, including more than 200 F-16s of its own. Northern Israel is well within the combat radius of the F-16s and with a fleet of 7 tanker aircraft the Turks could easily reach all of Israel if they wanted. The Turks also have four airborne early warning and control aircraft, implying a level of sophistication in air warfare Israel has never had to face before.
At sea the balance of power is much more one-sided. Isreal's navy, while professional and experienced, is tiny. It has just three submarines and three corvettes as well as some missile boats. The Turkish navy has 19 frigates , all of which are larger than any ship in Israel's Navy as well as some corvettes and missile boats of its own. The Turks also have 14 submarines.
Any skirmish between the two countries would likely only involve naval and air forces, but it's worth noting that Turkey's army is far larger than anything Isreal could field and is professional and capable.
All this leaves aside the possible NATO consequences of Israel's act. It's unlikely Turkey would ask for direct aid from its NATO allies in this case, but it could clearly expect that no NATO country, including the USA, would provide any help to Israel.
Lastly, Israel cannot threaten to use its nuclear weapons against Turkey because of the NATO nuclear umbrella, so this confrontation will turn on conventional capabilities alone.
It would be wise for the Israeli government to consider the risks of its current confrontation with Turkey and whether or not it might be prudent to beat a hasty retreat making any and all apologies required.
Turkey seems to be hugely PO'd over this and unlike the Arab countries it has the military wherewithall to make its displeasure known.