The Majestic does have more character. It's been remodeled a few times over the years (have never stayed there). Caravelle has also been remodeled, and yes I'd say it looks more like a USA style hotel.

That being said, it has better restaurants (and location IMO, directly across from the Opera House. Staying on the river in Saigon isn't anything special). Rooms were nice last time I was there (8 years ago as now I when I'm there I stay at the Sheraton). And as I mentioned, the Saigon Saigon bar is a nice place to relax and have a drink. If money isn't an issue, I'd stay at the Caravelle.