Completely different. The Empyrean universe came into being (AFAIK) several years before Rob & Brian began developing EP, and although Brian did sit in on an Empyrean game once, it wasn't an influence on Eclipse Phase. However, Empyrean is a trans/posthuman setting, and EP's mechanics are a near-perfect fit for the game.
Some of the core concepts of Empyrean are nearly the opposite of what EP posits. Just to give two examples, singularity events in the Empyrean universe have been extremely rare, with humanity never having been through one (as far as anyone knows... it's far enough in the future that many cultures aren't even sure where Terra was anymore, or if it was real). As a second example, Empyrean has a lot of technological scarcity built into it, rather than the open source free for all of EP, such that the challenges and opportunities of interstellar trade have a great deal to do with local technology levels. (This will sound familiar if you've read Vinge's A Deepness in the Sky).
Derek & I hadn't planned to publish Empyrean, as we're both more focused on writing fiction. However, we had so much material written, we didn't want to let it languish. Porting it to EP is a relatively easy way to put it out there for people to use without embarking on the epic project of starting a company just so that we can develop an original RPG (which, as you probably know, is pretty much what you have to do to get an original game out there).