Hi there, Justin.
When I bought my first "extended range" bass, I went through the same tough decision making process that you did. What are the benefits to each? What best suits what I want to do? There is alot to consider.
In the end, I went with a six string bass the first time. I thought "hey, the only difference is the extra string, and if I don't use it, I can ignore it". That isn't so much the case. The more I played the bass, the less I used the C string, and the more it started to annoy me. After a few months, I coudln't stand it anymore and swore off extended range basses, thinking that the same would be true for a 5 string.
A couple years later, I had the opportunity to pick up an American 5 string jazz bass, so I decided to give it another shot. This time, it was a whole different story. The more I used the bass, the more I loved having the fifth string. Not only for the lower notes it provided, but also for the ability to play the same songs I used to play, but higher up the neck but still with the same notes. Now, after 2 years, I barely touch 4 string basses anymore. The string spacing, the size of the neck, everything just feels right on a 5 string to me now, which is why my most recent bass was a beautiful 5 string Stingray.
I'll never buy another six though.
Hope that helps! If you have any questions I'd be happy to answer.