This was our first time cruising on Carnival. We were a little concerned about their "party" reputation since we were traveling with kids, but because we could drive to their port in New Orleans we chose them over flying to a Florida port.
Overall we had a great time and would gladly sail with Carnival again. The Triumph is an older ship and lacked some of the amenities that we've had on other cruises (rock wall, ice skating). The pools were also smaller than we've seen on other ships. However, it was very clean and the service was great. The food was very good - better than other cruises I've been on. They had several specialty stations (burgers, oriental, pizza) that were good.
My 6 year old really enjoyed the Camp Carnival activities. However, my 9 & 12 year olds weren't nearly as interested in their programs. The evening entertainment ranged from a great magician to other shows that were just ok. I don't think the programing was as good as what I've experienced on Royal Caribbean.
Even though it was a spring break trip, I thought the other passengers were very well behaved. I didn't see any rowdy behavior or excessive drunkeness that I was worried about.
The New Orleans port is VERY slow. Embarking and disembarking were by far the worst I've ever experienced.
Overall, I'd recommend this ship. It was priced right for the experience.