Those solicitations lie like filthy dogs. Hal has never appeared in GLC.
As for which one to get, it honestly, totally depends on what you want to read about. Green Lantern Corps is all about the Green Lantern Corps as a corps; it's an ensemble book and focuses a lot on more on, well, every single Green Lantern that's not Hal or John. It's about the adventures of the newcomers like Soranik Natu and Sodomy Yat, as well as longtime veterans like Kilowog and Arisia. It used to be much more of a Guy Gardner series since he was the most well-known character on the book, but Kyle Rayner joined the cast at the end of the Sinestro Corps War event and now it's more or less "their" series.
Green Lantern is Hal's solo series, with John Stewart as an occasional guest-star. (Guy appeared sometimes as well, near the beginning) It's about Hal Jordan punching things. That's...well, that's it really, what more to say? If you like Hal Jordan at all, you'll probably enjoy this book. It's fairly straightforward and quite easy to get into; almost any arc is a decent jumping-on point. It also has the distinction of having more to do with Blackest Night; most of the setup for BN occurred in this book, with several exceptions that happened in GLC. Consult
this sexy sticky for more info on that.
I personally, vastly prefer GLC to the point that it is my single favorite series on the shelves. I find it incredibly well-written and has gotten me to care about all these characters that aren't famous or mainstream or anything, but no less fun to read about. But, again, it's completely up to what you personally are interested in, because it's not like how Detective Comics and Batman are both about Batman, just written differently by different people. GL and GLC are about completely different characters literally set in different corners of the universe, despite the fact that they're all Green Lanterns.
Honestly, why not get both? Getting one doesn't preclude getting the other, just because they're both about the Green Lantern corner of the DCU. Especially considering the fact that the two series are probably going to cross over more often once the Brightest Day series starts, since BD is co-written by the guys who write GL and GLC.