Depends on the head. 88 with a stock head, not a chance. 124 with a BVH would blow it away more. Stock head vs. stock head, the 124 would win. 124 with stock head vs. 88 w/ superhead... probably the 88 then.
a chinese 125 motor that is running properly and has the correct compression (i.e. little johhny pitbike rider never cleaned his air filter and its smoking like a 2 stroke) will walk away from an 88cc anything. Your honda 88 is a 3 speed (unless its a 4 thousand dollar 88cc motor... but thats just dumb) and the 125 is a 4 speed. I dont know what kind of racing you are talking about. Drag racing the bikes... the 125 will dominate. The 88 might have an advantage on a super tight track... it all depends on rider skill.
If its a stock head 88... you might as well race a pedal bike against the 125. Race head makes a big difference... but without the long stroke of the 125, it has no torque.
To make serious power out of an 88, guys tend to do things like run big carbs, wild cams, pistons that require race gas... etc. etc. That usually makes for a motor thats all top end but is pretty doggy down low in relation to a motor with a longer stroke. A smooth running chinese 125 is hard to beat with a budget honda... i'll leave it at that.
in a drag race the 125 should win if motors were both tuned correctly. Pretty hard to compete with a 4 speed. On my 88 with a race head I have spanked bikes with bigger motors but it is due to experience more than the power of the motor. My "dumb" motor with only the honda cases left stock will crush a stock Thumpstar, but who wants a "dumb" modded honda motor?
I'm with firepower354... I'd like to see the video, please?