For feedback, wrapless.
For no maintenance, easy to clean - wrapless.
For feel consistency, wrapless. With the exception of cues like the Predator Roadline where the wrap is down where it should be where most people grip.
For grip, linen. Although not a big deal...I can remember only twice in 20 years where for some reason, my grip hand started sweating abnormally more and the cue actually felt slippery. Wasn't a pressure situation either. Leather can get slick in those scenarios too.
For cleanliness, wrapless. This is the main reason I like wrapless cues. I don't smoke. When I'd shoot with my linen and leather wrapped cues at the pool room, they would soak in the nasty cigarette stench. Then at home, playing on my table - I would get an occasional whiff of smoke / ashtray scent. Which is distracting because you don't expect it in a smoke-free, clean home. You really realize how bad your gear smells when outside that environment. Another reason why I got rid of my expensive leather cases, and prefer synthetics. They can actually be cleaned.
For aesthetics....I like wrapless if the design warrants it, such as sneakies and plain cues. For a design that has a wrap, leather is far better looking to me.
I don't dislike linen, but most linen wraps are inferior. A very high quality linen wrap, with a very well pressed, pro installation has a great feel.
For robustness, leather. Get a ding on a wrapless, and you'll feel it. A ding on a linen can also be felt, or worse - if it breaks the linen you can really feel it. Especially if the linen gets a fuzzball. Leather can take a ding and it absorbs it. Being textured, it all blends in.
For stability, wrapless. Most cues with a linen or leather wrap are not finished under the wrap. Thus, the wood can and does change in moisture content over time and environment. The butt is not completely "sealed" ...and this can cause very slight warpage.