The Infinity Ward Engine is a very bare bones, very streamlined engine that exists for the express purpose of creating three kinds of games--shooters, shooters, and shooters. It's been employed exclusively in-house and features no mod tools. I don't believe they even license it out to studios outside Activision, actually. Not that you'd want to mod with it, it's extraordinarily rigid; it's not just that it's only made for shooters, it's that it's only made for Call of Duty. The developers themselves say so--but that's how they like it. It's a tool expressly designed for their workflow and the types of games that they make and that they know they'll be making until the end of time, and it works well for them, enabling them to develop fairly high-quality content in extremely short cycles. Plus, since it doesn't have a lot of overhead from features their games don't need, it runs super-efficiently. It's the way any proprietary engine should be.
The Source engine, while not precisely 100% open to all users, does have an SDK available to anyone on Steam who wants to futz with it. If you're a computer scientist with expertise in C++, at least. Still, it's widely available and has represented a wide variety of mods and games, including Valve's catalogue, third-party projects like Dino D-Day, Darwinia, and Flipside, as well as Vindictus, an action-MMO that takes advantage of Source's physics engine, and Zeno Clash, a first-person beat-'em-up with a unique, almost Jim Henson-like atmosphere and a brutal combat system. It's a versatile engine and it's proven it, though it shows its age and feels more than a little rough around the edges the more it gets stretched. As a tool it's a bear to try and work with. Modern features like real-time preview haven't been worked in since its inception, and it still feels like trying to build with the Quake engine in a lot of ways, depending very strongly on constructive solid geometry where modern engines depend more strongly on static meshes.
Oddly enough, both engines are very similar in that last regard. Where Unreal Engine and CryEngine maps are built on the principle of modularity, Infinity Ward Engine-based games do not feature any modular buildings or assets. There's a collection of repeatable props, of course, but environments in their games are more or less hand-crafted with incredible attention to detail, much in the same way that Valve's games are, but taken to a somewhat greater extreme.
*shrug*
I don't really have an opinion either way. They're both fascinating pieces of tech that I've got some respect for, and I just like talking about this stuff. Personally I wouldn't develop a game with either. I'd sooner get my own proprietary engine together, or just go with Unreal, as it is the engine that I myself am the most familiar with.