I've been to both places, several times. In general, the more undeveloped areas of T&C have better diving. Dominica is a far more beautiful place, more like a remote south sea island than a busy dive resort, which T&C can be at times. These islands are also flat, dry, and to my eye rather barren.
Dominica is wild and wonderful topside, a feast for all the senses, but it is a volcanic island with rapidly sloping sides that plunge into abyssal depths very quicky. The coral band around the island is consequently thin, and most of the bottom structure is boulders, encrusted big rocks, and small rocks. Not much coral sand anywhere. Still, I prefer Dominica. The number of dive sites is much smaller, but some are spectacular. Add to that the clear warm rivers, the seemingly endless rain forest, the parrots, the boa constrictors, and the fact that the population is small and the number of tourists tiny, and you have something unique in the Caribbean. It rains more in Dominica, and is frequently overcast. T&C is much sunnier, usually. Another thing: T&C is infested with Lionfish. There are far fewer in Dominica. Finally, T&C is easier to get to.