mc,
talking of styles:
samba and bossa: better on the Tyros
merengue and cumbia: better on the SD1
(the SD1 has also a greater number of latin styles, including some unusual ones).

Speaking of sounds, the Tyros has much better electric pianos, acoustic and electric guitars, strings, pads and synth sounds.
The SD1 has a good acoustic piano, a good vibraphone, good organs and good brass. Speaking of drums, both keyboards have great snares and kicks, but when it comes to sounds like cymbals, cabasa, agogo, etc, the Tyros sounds more realistic.
More in general, if you compare the two keyboards side by side, you will notice that the Tyros has a greater content in high frequencies, while the SD1 seems to "die" at about 12 KHz. I think that this is due to the fact that, to save memory, the sounds of the SD1 have not been sampled at 44kHz.
Good luck with your choice.
Andrea