I have both, and well... most of the guys here are spot on the money. They are very different instruments, and make no mistake, they are that. Instruments meant to be played more than controllers. However, depending on what you want to do, either are really great and have things the other lack.
The quneo presets honestly suck. They really do, except possibly for the launchpad emulation, but... it is soooo easy to program, that coming up with your own custom layout is pretty trivial, and you can totally wrap it around your play style, but... It blows for automation and recording. I'm sorry. I love mine, but it just doesn't lend itself well to mapping FX, fine grained control of faders, etc. For jamming, presenting a live set you've worked out or whatnot, it just can't be beat for the form factor, lightness, ease of use, and it slips into any laptop bag pocket. For that, it rocks. With the remote pack, you can even take it around a stage. It's cool as hell.
However, creating stuff from scratch, working on ideas, recording automation, playing in key, and deep workflow, you can't beat Push. You just can't. It's the fastest way to get from idea to recorded track. Live however, it's heavy, the velocity sensitive buttons are great, but not as expressive, there's no x/y control of any type, so multi dynamic FX are a bit of a b*tch to work with, and it's not got so much a learning curve as a learning brick wall. Seriously, it takes some geting used to. Also it's nowhere near as customizeable as quneo. Still, if you want to jam in the studio or with a friend, or really, really quickly work out a song from an idea, quneo doesn't come anywhere close to Push's capabilities.
They are very different tools designed for very different tasks. So comparing them is hard to do.
If you want to get a quneo useable IMHO, you are gonna have to spend some time in the editor tuning it up for your use, but it's inexpensive compared to push, fits in a kit bag like nothing else, and is a great companion for the road. So if you're on a budget, I might start there. If you're gonna be spending more time in the studio than playing live, or have a bigger budget, then Push is a clear winner.
Novation just launched the LaunchPad Pro which is their answer to Push, and has many of the same features of either platform, but not full, and is mid way in price.
I had a chance to fiddle with one lately, and if I didn't already have a Push, it would be my choice over either. It lacks the depth of Push, but has a great form factor and ease of use that Quneo doesn't without a lot of editing.
If you go the Quneo route, check out enhanced note mode - a new plugin / config. It's pretty helpful.
Sorry if it's vague, but I can't call a clear winner, because they are both so useful, but for totally different things. I think it really depends on how you are expecting to work and your budget. I love them both, but for different reasons.