Fortunately, both Sun Tzu and a lot of other strategists' works are available and out of copyright, so you can compare them yourself if you'd like.

I'd say that the fundamental ideas are not different. There are different matters of emphasis -- but this matters vary more from work to work, not necessarily as some great dichotomy between "Western" and "Eastern" tactics or strategies. For example, I think that if you read Sun Tzu's Art of War and Vegetius's On Military Matters, you'll see a lot of common ground, but if you read Machiavelli's The Prince, you'll find something quite different from Sun Tzu or Vegetius. It's not that Machiavelli necessarily thought Sun Tzu or Vegetius were wrong -- he was just dealing with problems of a different level.

There are some cases where Sun Tzu frames things from the perspective of "here are some nasty things you can do to the enemy," while Vegetius frames them from the perspective of "here are some nasty things that the enemy might try against you," or vice versa. For example:

Sun Tzu:

23: Throw your soldiers into positions whence there is no escape, and they will prefer death to flight. If they will face death, there is nothing they may not achieve. Officers and men alike will put forth their uttermost strength.

24: Soldiers when in desperate straits lose the sense of fear. If there is no place of refuge, they will stand firm. If they are in hostile country, they will show a stubborn front. If there is no help for it, they will fight hard.

Vegetius:

THE FLIGHT OF AN ENEMY SHOULD NOT BE PREVENTED, BUT FACILITATED

Generals unskilled in war think a victory incomplete unless the enemy are so straightened in their ground or so entirely surrounded by numbers as to have no possibility of escape. But in such situation, where no hopes remain, fear itself will arm an enemy and despair inspires courage. When men find they must inevitably perish, they willingly resolve to die with their comrades and with their arms in their hands. The maxim of Scipio, that a golden bridge should be made for a flying enemy, has much been commended. For when they have free room to escape they think of nothing but how to save themselves by flight, and the confusion becoming general, great numbers are cut to pieces. The pursuers can be in no danger when the vanquished have thrown away their arms for greater haste. In this case the greater the number of the flying army, the greater the slaughter. Numbers are of no signification where troops once thrown into consternation are equally terrified at the sight of the enemy as at their weapons. But on the contrary, men when shut up, although weak and few in number, become a match for the enemy from this very reflection, that they have no resource but in despair.

Another loose parallel:

Sun Tzu:

2: Hence to fight and conquer in all your battles is not supreme excellence; supreme excellence consists in breaking the enemy's resistance without fighting.

Vegetius:

To distress the enemy more by famine than the sword is a mark of consummate skill.