So I'll take on your last questions first. Politics in both areas are a little mixed. Both the Triangle and Metrolina tend to be Democratic strongholds as urban areas tend to be. Go out 30 minutes to an hour, though, and you hit more rural and more conservative areas. I'm biracial and I'm in an interracial marriage (by definition) - neither my wife nor I have had any sort of negative reaction to us when we're out in public. Neighborhoods to avoid in the Triangle is a little trickier. If you're talking Raleigh, the area to avoid is Southeast Raleigh. Portions of Raleigh off of Capital Boulevard are also not the greatest. The most desirable areas of Raleigh are what's termed "ITB" Raleigh - the portion of Raleigh that's inside the I-440 beltline - and North Raleigh. Durham is a little more patchy - the area around Southpoint Mall is nice as well as the general area around RTP. There's also some neighborhoods near Brier Creek that are quite nice - DaveG and I both live in one of those neighborhoods. Go 5 minutes west towards downtown though and you hit some not as nice areas. Chapel Hill and Cary in general are nice areas. I can't speak for some of the other Triangle component towns (Knightdale, Wake Forest, Apex, Fuquay-Varina, Clayton, Garner, Holly Springs, etc).
As for differences between Charlotte and Raleigh I'll try to put it out like this - both are excellent cities. Charlotte's economy is more built on banking (even after the recession) and being a HQ city for multinational corporations. The Triangle's economy is built on state government, education, information technology, and biotechnology. I think culture is more similar than different - both have planned neighborhoods filled with McMansions and chain stores/restaurants but also really unique funky neighborhoods and independently owned stores and restaurants. In terms of ease of life I think I'd give the edge to the Triangle. Cost of living is a little lower here, it seems a little more laid back, and traffic isn't as much of a problem (I-40 at rush hour aside).
I lived in Charlotte for the first 18 years of my life then in Raleigh for the next 7. My parents still live in the Charlotte area and in fact I'll be back there tomorrow. I have a lot of personal preferences and biases on this issue so things could be completely different for you. That said, I absolutely loved living in Raleigh and it is one of the few places in the south I would move to. I never liked Charlotte, and while it has improved, I don't think I would ever want to live there.
I'm a city guy (if that's not clear based on where I live now) so my perspective is coming purely from someone who wants to live in a fairly urban area with some walkability in places. That pretty much limits to you to the downtown area in both of these cities. In Charlotte, the downtown is bigger. It's new, it's fancy, there are bigger buildings. There's light rail, and downtown sports venues. Definite wins for Charlotte over Raleigh. Yet, it's completely soulless. Downtown Charlotte has never offered anything for me. It's a place for the banking crowd, the frat brothers, the conservative businessman. All of the cool restaurants, bars, and neighborhoods that fit my style are spread out in the rest of the city, disconnected from each other.
Not so in Raleigh. Everything for me is in the downtown area. The downtown is small but one of the most lively I've seen in one of its size. Awesome local restaurants, bars, cafes, art galleries, etc., all at a much more human scale than Charlotte's Atlanta-imitation. No bands I liked ever came to Charlotte. They were always in Raleigh, Durham, and Chapel Hill. I also always felt like the Raleigh area did a better job of blending a city feel with laid back southern hospitality.
Ultimately, this is all a matter of opinion that is greatly dependent on personal preferences. I think for me it just came down to the fact that the prominent industries in Raleigh (higher education, technology, healthcare) were populated with people that were more of a match for me than Charlotte (finance, energy).
Both of you nailed it. I grew up in Raleigh, spent 4 years in Charlotte after college, then moved back to Raleigh about a year and a half ago. I found Charlotte to have a busier, more bustling pace about it than Raleigh, even though the areas are basically the same size. Charlotte's economy is focused more on banking and big business than Raleigh's; opportunities in law are probably similar in both cities, but if there's a particular area of law you deal in, one might be better than the other.
I agree with the sentiment about downtown Charlotte having no soul - there is stuff to do, but it's mostly either bars/restaurants or the kind of thing only you do once (Discovery Place, NASCAR HOF, etc.). It's completely dead on a Sunday unless the Panthers are playing. They knocked down everything that had character to make way for bigger and better things; Latta Arcade, the Dunhill Hotel, an old firehouse, and a few churches are basically the last interesting relics of another era still standing. You also have the ruins of Carolina Theater, but it's so dilapidated that you would never know of its significance if you didn't do any research. Granted, downtown Charlotte badly needed revitalization 20-30 years ago, but they went scorched earth rather than renovating and repurposing (partly because the banks started one-upping each other to see who could build the biggest building). In short, it's walkable, but you'll probably only find yourself walking between work, restaurants, bars, and the arena. It's exciting at first, but once I had walked by it all for the 100th time, I started to need a reason to go there. I couldn't just hang out there anymore.
The inner-lying former streetcar suburbs have much more soul and are where you'll find most of the good cultural stuff and hole-in-the-wall places. Neighborhoods like South End, Elizabeth, Plaza Midwood, NoDa (North Davidson), and Dilworth have plenty of great places to while away an afternoon or evening. Charlotte may have a little more of that than Raleigh, but it's easy enough to find it here if you know where to look - as GP said, there's a lot of it inside the beltline.
Raleigh doesn't have as busy of a downtown area, but it's much better-preserved and has a better variety of things to do (art galleries, music and performing arts venues, etc.). Downtown Charlotte is a reflection of its status as a medium city that's trying to be a big city; Raleigh is content to let growth come naturally and is in no rush to knock anything over just because it's old. Business growth also seems to be spread around town rather than concentrated in the central business district, unlike Charlotte (not that one way is better than the other; there are advantages to both). I do wish we had public transit to shuttle us downtown, but it's easy enough to get around by car.
As for other neighborhoods, Charlotte is a patchwork of good and bad that can change in about 30 seconds' drive, but Raleigh is easier to paint with a broad brush as GP described. Generally speaking, though, in Charlotte you might as well avoid most of the area that's inside of I-485 and west of Tryon, at least until you get up past about Sunset Road or WT Harris. On the north side of town, the university area has more bad neighborhoods than good until you pass 485. There are some less-than-nice pockets in east and south Charlotte as well, especially along Independence and near Eastland Mall, but if you're looking for a decent neighborhood, go there, outside 485, or up 77 around Northlake and on up. Rush hour on 77 north of town is awful, though.