I can’t give you advice on the hotels themselves (although I hear and read that the red interior of the Camper’s rooms is a bit too much “design” for some). But when it comes to the location, there is a clear difference.
Casa Camper is in the old town (narrow streets, no traffic), which I can imagine might be an attraction on itself for someone from the US. Don’t worry about the “issues” in el Raval. When people mention this they normally talk about the lower part of el Raval (towards the port), which was historically the red light district of Barcelona. This is not the area where Casa Camper is situated. (But even that lower part is not really dangerous; it might at most be a bit intimidating for those not used to big city life…)
The Alma is indeed in a “better” neighbourhood, and it’s also close to some attractions you’d probably like to visit. But the area itself is more like a normal city (with straight wide streets and lots of traffic). The advantage of that area is that it’s less touristic; so you’ll see more of the “normal” city life of the city. Also, there are a lot more good restaurants within a few blocks of the Alma. (In the old city lots of restaurants now seem to exist for tourists only, which has a negative effect on the quality. But there are still some good places to be found…)
Personally I prefer the area of the Alma (which for me is the real city centre; most locals tend to avoid the old town – the touristic centre - now). But for a first visit to Barcelona I would probably prefer staying in el Raval anyway. No simple clear answer I’m afraid…