Vegas is definitely the best bang for the buck. However, I use Premier. Though you could probably create a similar looking project in either, Premier's tools are far superior IMO. I've also had a decent amount of exposure to Final Cut while taking classes at a university. Final Cut and Premier seem to be set up fairly similar. Vegas is definitely different, not that that's bad. Since Final Cut only works on a Mac, I won't mention it. As far as Avid is concerned, it has a great reputation, but I don't have any personal experience using Avid. So I'll just talk about Vegas and Premier.
It's been a while since I used Vegas so I could be wrong about some of these features...
In a Premier project a timeline is an object, you can have as many timelines as you want in a project and nest them. Therefore, you can easily break up a project into specific parts, each on their own timeline and just nest each of these parts into a final timeline, all in one project. This makes for a professional and easy workflow. All the timelines are available in tabs in the same project. I believe Vegas supports nesting of projects now, but the implementation to me seems very lacking in comparison. It means you have to work on each piece of the larger project using many smaller projects.
Both Vegas and Premier support key frames for manipulating parameter automation. However, Vegas's implementation totally blows in my opinion. They are difficult to work with and are totally unorganized.
Premier’s tool set is very organized and easy to use. For instance if you want to stretch a piece of video to fit into a specific time slot, just click the tool and drag the end of the clip into place. Done. It's very difficult to do some simple things like this in Vegas. By default clip looping is turned on in Vegas, which can make working with clips a pain, so in this instance you would have to create a subclip and guess at changing the playback speed to fit the clip. Almost impossible do as I mentioned with Premier.
I could go on about the list of tool comparisons but I don't want to try and think of all of them off the top of my head and I think you get the idea. It took me a while to come to these conclusions. It wasn't like I spent an hour using each program and determined I like Premier better. It was over years of using them.
Again, this is just my opinion and like I said, it's been a while since using Vegas so things may have changed considerably. Vegas is definitely a good program, and like I said the best bang for the buck. I personally like the tools in Premier. Also Premiers integration with the other Adobe products is very good, like in Adobe Creative Suite. However, it is very expensive and may not be necessary for what you need.