I've had the shorts for over a month now, and have taken them on a number of runs in different weather, and they have felt absolutely great, like a second skin. I'm not sure about the compression bit, but it does hug the thighs quite nicely and doesn't move around. Pockets are a great thing to have, although the phone pocket can only fit a small phone. I'd definitely recommend them.
That said, a couple suggestion for 2XU:
The sizing is a bit confusing. On the website, the sizing was based on weight and height, which for me it got completely wrong. I was then sent another different size system, and then on the box there was yet another. It would be helpful to have a consistent sizing system, ideally by measurements and not height / weight. For reference I'm 5"6 and 130lb, and the small ended up fitting me well (it may be cause I'm overall more muscular?).
Second, in your next iteration, pockets - they're great, but hard to find and dig things out of when I run (I keep having to stop and try to find what I have stashed, or try to stash things back. 2 larger zip pockets would be helpful - one to fit a larger phone, and one smaller one for the smaller items. Even a side pocket if it's feasible? Pockets are awesome.