^^ This is correct.
The P3 Tualatin 512K was a beast for the time, it was just overpriced and impractical for home users (not to mention tualatin-compatible Socket 370 boards usually meant buying a new one even for owners of relatively recent P3 ~1ghz builds. Tualatin was .13mu process tech, and it allowed for 512k of full-speed cache, whereas the older Coppermine was .18mu just like Thunderbird and was limited to 256k L2.
I would put them this way .. P3 1.4S (512K L2) slightly faster than Athlon 1400 (much much much cooler though), and about equal in most circumstances to 1600+.
The 1400 Thunderbird was a furnace, and nearly as bad/desperate as the P3 1.13 Coppermine. They just shouldn't have attempted it. I've only seen one in the wild that worked at stock clocks with the stock cooler, and not for very long. I had one and ended up having to downclock it to 1050mhz just to get it stable under a thermalright XP-90 and 5000rpm fan, lol. That was also the bad old days of the non-IHS chips that cracked quite easily just installing a heatsink and following proper directions for heatsinks that were labeled Socket A/462 compatible. God forbid you try to install a golden orb, hah. *crack*. I had much much better luck with the Athlon XP chips in terms of reliability/durability, and they performed really well.