If you don't overclock....
Those are the key words right there. Given that, it's the Barton hands down because of the 512k L2 cache (vs. 256k on the Tbred) and the 166 FSB (vs. the 133 FSB of the Tbred).
Even with overclocking, most 2500+ Bartons are hitting 3200+ speeds (2.2ghz) with good boards and RAM. If you are absolutely not planning to OC, then I'd consider spending a little more and go for the 2600+ or 2800+ Bartons (at least).