I use this one to record vocals and voice overs mostly. Also electric guitars. I have used it during mixing to maximize drums or other material, which it's really good for.
I think it has a sort of a vintage sound, which counteracts nicely the digital, sometimes too pristine nature of modern recordings. For example, 99% of the time I record with an ELAM251 clone, which I really like, but has an extended HF range. I have set the sidechain detector of the COMP 3A to maximum HF, which means that it will react more to high frequency content. In this way, it pushes literally warms up the signal a bit, by compressing the upper range, and helps with strident or sibilant parts of the speech or any delivery.
The other thing is, it really helps with recording dynamic parts. You can compress a vocal with 20dB, and it is not exactly transparent, but too my ears, the compression and the coloration is almost always preferable.
I intend to get one more of these, or maybe a Comp 2A.