These are both good boards, I have used both with great success. They are reliable and stable. I prefer the Abit BE6-II because of the onboard UDMA-66 controller. The BE6-II is also better geared to the overclocking crowd with its extensive BIOS settings.
It's a dog eat dog world out there, and there isn't enough dog to go around. So get as much dog as you can, before all the dogs gone.
You need to go with the Abit BE6-2 motherboard. Thanks to Abits constant updating or their BIOS's the board can 133 Front Side Bus without any problem and has Ultra DMA 66 Support which is very nice. Also if you plan to overclock your system the Abit board will blow away the Asus P3BF because of it sheer capablities.
"640K ought to be enough for anybody." - Bill Gates, 1981