Before you get any further, let me provide this bit of context. Israel is the size of New Jersey. China is the world's third largest country with almost a sixth of the world's population. You're asking for a military comparison between those two.

SECOND EDIT: The CIA Factbook estimates a 250x discrepancy in potential combat forces, with about 3.4 million for available and 2.9 million fit for Israel to deploy as compared to 840 million available and 600 million fit for China to deploy.

With that in mind...

It's sort of a tricky question to answer, in part because of the general lack of conventional wars recently. Israel has permanent, asymmetric warfare being waged against them, with occasional operations to remove Hamas's missile platforms. China has spent a while shaking their military penis at the US and at their neighbors.

First, some facts:

• Israel inarguably has the strongest military for their size in the world. No other country even roughly their size  shows up on the who's who of military powers except England, and they're scaling back their military to cut costs.
• Israel's spent the last few decades fighting asymmetric warfare.
• Israel is made of reservists; an overwhelming majority of the populace could be called on with days' notice.
• Israel has Iron Dome, the only effective missile defense of its kind.
• China has more money and manpower to throw at the problem.

But there are a still lot of unanswered (and unanswerable) questions:

• Whose planes are better? Whose tanks are better? Whose missiles are better?
• Is Israel's technological advantage large enough to overcome their lack of manpower?
• What's the battleground? Israel has considerably more expertise fighting in deserts than almost every other major power, for example.
• How is the fight being carried out? Is it an infantry battle? A tank blitz? Dogfighting? Urban warfare? A missile exchange?
• How are they getting there? Does one side have to haul ass before the fight even starts?
• Who's pitching in, if anyone? Does Israel also have to fend off their neighbors? Is the US pitching in for them?
• What's the objective? Are they going to start annihilating each others' populace, or is this purely a professional thing?
• Imagine if they all got magically transported somewhere. Israel would probably win tank and aircraft jousts close to 10 times in 10. But, Israel's so wildly outnumbered that such information is surprisingly hard to weight.

So my answer would be that unless you artificially constrain the question, there isn'tan answer. 

Besides, those two countries are very far apart. If China wanted Israel dead, they'd sell Hezbollah a nuke, instead of something with a return-to-sender address like a missile or a plane.

I vote for Israel.
 
China will never be conquered by any large populations (Huns, Turks and Japanese), but by smaller nations like the Xianbei, Mongols and Manchu. I believe Isreal is even stronger than the latter. So with that having been said, Israel would win just as Mongol and Manchu did. And 100 years later, Jews will become the 57th ethnic group that speak Chinese & eat the famous pork meat of China.
 
You can conquer Rome, but you can't refuse having Latin words come into your language, and their very delicious foods enter through your stomach. The same is true for China. Therefore, if you refuse to give up the Hebrew language that you revived through thick and thin, (which was jealousyly admired by the Manchus), please don't let Conquering China come into your mind.
 
That's our lesson from our own history. I shared it with you.

There are already loads of answers to this question, some of which are pretty good. However, most of the answers written before mine are way off base by mentioning the size of China versus the size of Israel or relative populations. Those factors happen to be pretty insignificant in this consideration in the most likely scenario of China trying to invade Israel. As are cyber warfare considerations, since "war" still means with weapons in the real world and not "cyberwar."

The question itself is really too vague because a lot depends on initial conditions of an such war.

So let's break this down into a few separate questions:
1. Could China successfully invade Israel?
Almost certainly not. While it is possible in a bizarro alternate Earth to imagine China trying to invade Israel, how will Chinese forces get there? The overland route would go through hostile nations the Chinese would not care to fight on the way and even if they did, it would take a long time and Israel would have plenty of time to prepare. China could not effectively move and supply its entire army--so the army that arrived at Israel would be just a fraction of its total strength, with supply lines too long and no natural air bases. Israeli equipment is more modern and their personnel better trained than China's--Israel could maul the Chinese forces that actually arrived at Israel in any such war. Note that it bears saying that neither of them would want to fight such a war.

The situation is even worse if China tried to invade Israel by sea. China's navy isn't all that awesome and certainly isn't ready to project power thousands of miles from home. The Israeli Air Force would send the Chinese fleet to the bottom of the Red Sea and there would be nothing the Chinese could do about it--even if the Saudi and Egyptian Air Forces flew out to protect the Chinese ships, they STILL would almost certainly get wiped out before delivering their troops.

2. Could Israel successfully invade China?
No way. In this case, the size and population of China really DO matter. Though first off the Israelis would have the problem of projecting power that far (and why would they even want to?). But if they managed to say, refuel their air force enough to make strikes against a Chinese city, they'd probably be a lot more successful than the Chinese would be the other way around. But so what? China really IS huge relative to Israel and there is no way for Israel to defeat them in battle by invading them. There just aren't enough Israelis to pull it off. (And again, why would they even want to?)

3. Could China and Israel engage in a nuclear war and if so, who would win?

Short answer: nobody knows. This is actually a realistic possibility as far as China definitely has missiles which can reach Israel and Israel's Jericho 3 missile supposedly can reach China. But as far as I know, the number of missiles and nuclear warheads Israel has is secret. And does Israel have a ballistic missile defense system? They have a defense against tactical missiles, perhaps the best in the world. So they might have a defense against incoming Chinese missiles. That along with excellent Israeli intelligence means it might at least be possible that Israel would know the Chinese are going to launch missiles in advance and take the missile sites out before they do--while simultaneously protecting themselves from any Chinese missiles that might be inbound. NOTE that the total number of Chinese nuclear warheads are thought to be in the hundreds, not in the thousands like the USA and Russia. It's actually possible Israel as many nukes as China has, though perhaps not likely.

Though having said that, in general a large country can absorb nuclear hits with at least some of its population surviving. Israel is so small only a few nuclear strikes would totally devastate the whole country. In general you'd have to say China would have a big advantage over Israel in a nuclear war. But we just don't know how it would turn out, because we don't know enough about Israeli nuclear weapons and ballistic missile defense capacities.

So would you go to war against Israel if you were China? No way. And I don't see it happening the other way around, either.

Active personnel:	1 281 900	2 300 000
Reserve personnel:	811 000	8 000 000
Available for military:	73 270 043	385 821 101

Military budget:	610 billion $	228 billion $
Percent of GDP:	3,1%	1,9%

Tanks:	6 393	7 760	×See current equipment
Armoured fighting vehicles:	41 760	6 000
Total artillery:	3 269	9 726
Self-propelled artillery:	950	1 710
Rocket artillery:	1 197	1 770

 

Air Forces

Total aircraft:	12 304	4 182
Fighter aircraft:	457	1 150
Multirole aircraf:	2 192	629
Attack aircraft:	587	270
Helicopters:	4 889	1 170

 

 

 Navy

Total naval:	437	780
Aircraftcarriers:	20	2
Destroyers:	85	36
Frigates:	0	54
Corvettes:	0	42
Submarines:	71	76

 

 

 

Military service

USA

18 years of age (17 years of age with parental consent) for male and female voluntary service; no conscription; maximum enlistment age 42 (Army), 27 (Air Force), 34 (Navy), 28 (Marines); service obligation 8 years, including 2-5 years active duty (Army), 2 years active (Navy), 4 years active (Air Force, Marines); DoD is eliminating prohibitions restricting women from assignments in units smaller than brigades or near combat units.

China

18-24 years of age for selective compulsory military service, with a 2-year service obligation; no minimum age for voluntary service (all officers are volunteers); 18-19 years of age for women high school graduates who meet requirements for specific military jobs; a recent military decision allows women in combat roles.