Being able to stay in the mainstream arcade market requires the distribution capabilities that really only SEGA Sammy still have (even Namco survives by being teamed up with them), so Tecmo had to follow the lead of Konami and Capcom in exiting.
Of course, the critical factor in a developer's support of any console comes down to the business side. Team Ninja has a lot more say in Tecmo's direction than the average developer, though, since team head Itagaki took on the overseeing of all Tecmo software as well. He trusts Microsoft to be ambitious in hardware design when they're seeking quality technology partners like nVidia and ATi. The team liked the Saturn too -- for as messy as it was in layout, it was designed like an arcade board with no expense spared in multitude of processors. And when Team Ninja, long time aficionados of SEGA's choices in arcade hardware, moved Dead or Alive 2 from Model 3 to Naomi/DC in 1998, they mentioned their admiration for the platform SEGA had put together for DC.
However, business concerns take precedent, and Tecmo was not going to go down with the DC or ignore the PS2 initially. With a mutually beneficial partnership to their respective businesses at work between them and Microsoft, though, they were also able to satisfy their preference in hardware by going with Xbox.