I grew up and Charlotte and have now lived in the Triangle for 11 years. I agree with many of the comments so far about Charlotte having a greater density of quality courses. However, I think the Triangle has a great disc golf scene, plenty of good courses if you extend to all of the counties in the Triangle, and there are a TON of new courses coming online this year and in the next couple. Here are just a few of the new courses I've heard about:
East Clayton (30 minutes from Raleigh)
Marsh Creek (in Raleigh)
West Cary (right in the middle of the Triangle, in between Raleigh, Durham, and Chapel Hill)
Forest Ridge (this will likely end up being 2 championship courses on Falls Lake, just north of Raleigh)
Rolesville (I'm working on getting a DG course to this Raleigh suburb and it's in the town's strategic plan)
DG absolutely shouldn't be the deciding factor in your decision as I feel that Raleigh has terrific disc golf and it's only getting better. I work in state government, so I have that bias towards Raleigh. I would base it on your work travel. If you're in Virginia and Maryland more than most other states, I'd definitely go with Raleigh.
As far as things to do, both towns have a lot to offer. Charlotte is more of a pro sports town with the Panthers, Hornets, and Knights (AAA baseball). The Triangle is much more of a college sports area (UNC, Duke, State), but also has the Hurricanes and a few minor league baseball (Durham Bulls, Carolina Mudcats) and soccer teams and the like.