Horace Silver was gigging in Cleveland circa 1957 when he heard The Three Sounds. He befriended Gene Harris and introduced him the next year to Alfred Lion. Before The Three Sounds signed to Blue Note, they played an extended gig in Washington D.C. backing Sonny Stitt. Both Kenny Burrell and Miles Davis heard that gig and supported their move to New York. Lion heard them play at The Offbeat Club in NYC and signed them soon thereafter. Francis Wolff took photos of the trio at The Offbeat, but to my knowledge there's no recording of that gig.
The trio broke up in 1967. Dowdy left first, to be replaced by Donald Bailey. Simpkins then took a gig with George Shearing in 1968, which lasted through 1974. The Three Sounds left Blue Note in 1962, recorded albums for Mercury and Verve, and then returned to Blue Note in 1966. Of their return, Michael Cuscuna wrote that "success had diluted the trio's original impact, and their repertoire had become overrun with fanciful, inferior pop tunes of the day." Can't disagree with that. But the 1958-1962 recordings are tight. I don't really hear a comparison with Red Garland, but I do hear a parallel with, say, Horace Parlan. For my own listening, however, I almost always choose The Three Sounds over a Parlan record.
Ranking The Three Sounds albums isn't exactly useful, and I haven't heard them all, but if I had to rank those that I know, it'd look like this:
1. Good Deal
2. Moods
3. It Just Got To Be
4. Feelin' Good
5. Black Orchid (with bonus tracks)
6. Babe's Blues (this album is actually bonus tracks from Hey There)
7. Here We Come
8. Bottoms Up!
9. Standards
(Those are all that I've heard. That's either just enough or perhaps too many.)