Definitely Sony Vegas, A few years ago I watched a very funny video titled "Idiots of Garrysmod". I loved the video so much I asked the creator what program he used and how difficult it was to learn it and he messaged me back giving me a link to Sony Vegas where I promptly bought it and started fiddling with it right away. It is as Dave said it is simply one of the best video editing software out there
They both have their positive aspects, but Sony Vegas is definitely the better choice for a beginner. Its compatibility with some editing software like after effects makes is that much easier to edit your films, and it's far more intuitive and user friendly. Go for Sony Vegas, you won't regret it.
Sony Vegas is the most complete video editing software out there, you should get it along with some good books on the matter, to help you learn its tricks.
I've used Sony vegas for over 10 years now, and I can say it is simly the easiest professional software you can step into - no learning curves, and it is the best video editing software for chopping music together. If you've used Sony Acid or any similar programs, you'll find it so easy to step into. After using Vegas for years, I found that Premiere was harder to step into, but just as powerful. Vegas is a lot easier to look at the timeline in my opinion - a big timeline and small video preview makes editing more streamlined than Premiere. Industry standard is to use Premiere, so if you want to get a job in design, learn the Adobe side of things. If it's just for home use, I'd say Vegas. You can get cheaper versions of both Premiere and Vegas from the vendor's site (slightly less features)
I've taught myself to use Vegas over the past few years always trying to outdo my last video with some new feature that I haven't tried before. There's a link to my channel to the left. I mainly make Minecraft videos and Nature Time Lapses, and I haven't hit any major walls where it felt like Vegas was holding me back.
I would say that it depends on what you're used to and what you will use them for. Adobe Premiere might be easier to use for those familiar with Photoshop. Sony Vegas renders videos faster, but Premiere is supposed to be more visually realistic.
I Would start with Premiere, only because you'll end up there eventually, you could also try Premiere elements as a bridge into Premiere Pro. Honestly, neither one is that hard to learn and you'll be better off getting the more commonly used software mastered even if it may be slightly more difficult to use.
I would actually start from the Windows 7 Version of Windows Movie Maker and figure out ALL of it's options and techniques first. Then move onto Sony Vegas.