In past distribution comparisons at Phoronix, the performance differences have been larger than what we experienced with Fedora 10 and Ubuntu 8.10. Both the x86 and x86_64 editions had performed nearly identical. In fact, the results are so close that it's hard to call a winner in any of the benchmarks. There's a few slight deviations in tests like the timed Gzip compression and BYTE Unix Benchmark, but nothing conclusive, at least with the hardware configuration we had used and the real-world tests conducted.
If you would like to see how your distribution performs, check out the Phoronix Test Suite. With the performance differences being minimal, it really comes to the feature set of each distribution and which one you are most familiar with (Ubuntu / Debian vs. Fedora / Red Hat) when deciding between these two popular Linux distributions.