I'm not a pro jazz player, but I play in my school jazz band, and gig around in combos and stuff. A lot of parts I get are overly detailed to the point that they are annoying to read. If you there is a specific way you want the piano to comp, like a special montuno pattern, or you really need the pianist to do double horn hit somewhere, than you should write it out, but in most cases the writing out the chords is all that's necessary. Often I will get a part in which the composer writes out note-by-note typical swing comping patterns every measure, instead of just letting the piano player do his thing. These parts often end up being 15 pages of notes, instead of what could have been 4-5 pages of chords.
The best way to improve your comping, once you know the basics, is by getting a fakebook and playing a bunch of tunes, preferably with other people, constantly experimenting with different voicings. Make sure you can play any chord in all it's inversions. be sure to build your chords off of not only 3rds, but 4ths and 5ths as well.
One way to look at jazz piano comping is that you always want to find the shortest path between chords. So let's say you're playing Cm7 to F7. The dryest, straightest way to play these chords is to just play them at root position: Cm7 being C-Eb-G-Bb, and F7 being F-A-C-Eb. But if you play this, you'll quickly notice it sounds awkward because there is such a big jump between the two chords. Instead of moving everything, let's look for common tones between the two chords, and keep them where they are, and then only move the notes that need moving. Starting on the Cm7 chord, we see that the C and the Eb are the 5 and 7 of the F7 chord, so we really just need to move the G and the Bb. The closest note to the G in the F7 chord is F, and the closest one to the Bb is A, so now we can go from Cm7 to F7 just by moving the top to notes down a whole step: C-Eb-G-Bb to C-Eb-F-A.
But this voicing still isn't great. Since the bass player probably has the root covered in the Cm7 chord, we can get rid of the C and add in the 9 just for colors sake. Let's use the voicing Bb-D-Eb-G. As you can see, we removed the root, added the 9 in the middle of the chord, and took the 7 to the bottom of the chord, creating a much hipper voicing. If we want to move that to F7, the only note we have to move to get the tonality is the Bb. The D can stay, as it's the 13 of the F7 chord, the Eb is the 7, and the G is the 9. You could argue that the Bb could stay as well, since it could be seen as the 11 of the F7 chord, and you'd be right. But if we want to stick in the 3rd (A), it'll probably conflict with the 11 (Bb) if we keep it in. Of course, we could keep the Bb, and not put in the A. Than the F7 chord would become an Fsus chord, and it is perfectly fine to make that substitution as long as it doesn't interfere with what someone else is playing. But for this demonstration, I'd like to keep it as an F7 chord, and move the Bb down to A. So for our new voicing of Cm7 to F7 we have Bb-D-Eb-G to A-D-Eb-G. Of course, you'll need the C and the F in the bass, but this should sound pretty good.
I think being able to comp is a useful skill for anyone looking to compose in any style. Once you've been creating harmonies on the spot playing jazz, creating harmonies for your pieces becomes extremely simple.