i was in your same position, cheaper vs. higher quality. i ended up shelling out for the 70-200 2.8, best decision ever. extremely sharp, very fast af and very accurate. can't say that i have every regretted it. i have heard that the f4ls are just as sharp, if not sharper, and are lighter. you wont regret the decision to get the 70-200, the f4ls go for about 500 used.
in my opinion, a lot of the time in photo equipment you get what you pay for. definitely worth the extra cash if you ask me (or any here with a 70-200)