Storj dev here. I talked about this elsewhere on BitcoinTalk, so will pull some excerpts here:

We're all about cooperation rather than competition. Unfortunately, this seems to be a thing in the decentralization space. Suffice to say, if both our projects are wildly successful then everyone in the decentralization ecosystem will benefit. As I like to say, in nature, polyculture systems work a lot better than monoculture systems. In our case, different teams with different backgrounds can try different paths of innovation.

One of the biggest differences between MaidSafe and Storj is that Storj takes advantage of blockchain technology and MaidSafe does not (as pointed out in one of their blog posts). David Irvine started working on MaidSafe back in 2006, before Satoshi even wrote the Bitcoin whitepaper. Because of that (even though they've integrated SafeCoins), they've gone along a different and unique evolutionary path.

Another difference, as some folks have pointed out, is that MaidSafe has been evolving their concept and organization for a while. Because of this, they've had time to build a pretty awesome team and work on some cool things like RUDP. I've had some exchanges with David and some MaidSafe folks on their forum and I think all of us share the vision and hope for what our platforms can accomplish. David and the MaidSafe team want to build a completely new kind of internet and have developed technologies to that end. Again, if they succeed we'll all be better for it.

Storj is a much younger project, really starting about 9 months ago, but we've made tremendous progress since that time. We're evolving on a different path than MaidSafe and are focusing on decentralized cloud storage at the present moment.

One of our strong desires is to make it unbelievably easy for non-crypto folks to use DriveShare and MetaDisk so UX is one of our core concerns.

You can check our whitepaper http://storj.io/storj.pdf for some more info and check our repos at http://github.com/storj.

There is certainly the possibility for integration of some of our front-end applications with MaidSafe (in addition to our own network) in the future. I think that in a world of open-source projects and decentralization, the more innovation the better.