I can't say specifically about competition on the 125's and 250F's because I can no longer compete due to arthritus in the right wrist so bad I can no longer make a 100 mile enduro or 3 (or even 2) hour hare scramble but that doesn't mean I can't still enjoy trail riding - the tighter and nastier the better.
I own one of each - a 125SX and a CRF250R. I do not ride moto - exclusively woods, and both bikes are a blast. I've always preferred the lightest bike possible that still had enough beans to be fun to ride although I did compete on many 250cc's and even 300's, but nothing larger. To pick just one bike, my all time favorite would have to be the 200EXC with power of the 250's and weight of the 125's - best of both worlds.
timr pretty much 'hits the bullseye' with his comments: I find the lighter bikes tire you out less - contrary to what many believe that the bigger motor is easier to ride & while that may be well and good, personally, I'd rather not fight the weight (constantly) of the "bigger" ride, and unless it's pretty open conditions - the power of today's 125's and baby 4 strokes do not put you at any disadvantage at all.
I'm not a light weight rider either at 195#, and both bikes do just fine with the 125 perhaps being a little more difficult to ride (well) because it likes to be ridden more aggressively - the 250 4stroke is probably a bit more forgiving if/when you start to get tired and get a little "lazy" with throttle and shifting.
Bottom line is that I'd highly recommend either bike for woods duty although I'll admit I'd probably also still have a 200 if the vibration didn't bother my arthritus so much.