I actually chart on both sites, myself. And occassionally there are disagreements. I've had FFlower switch to a date that concurs with FF and vice versa.
Why does it do that? The charting platform is looking for patterns in both cases. And sometimes, as you roll along with your cycle, it will say - hey, that looks like a more likely scenario for ovulation - I'm going to move the date. So that's the reason that these kinds of website do that switch-a-roo.
I'll take a look at your chart and make sure that there's not something more sinister going on with the software.