I am using Avalon for my Bucharest Romania, to Budapest Hungary. There were several reasons, one because the length of the cruise and land was a little shorter than AMA's. My husband couldn't get as much time off. Then I also got what I felt was a good discount of $1000 off, plus another $500 off from a special Facebook offer that Avalon had. On top of that I got another 5% for being a past guest.
I feel AMA and Avalon are very similar in food, entertainment, shore excursions, and their amenities of free flowing wine at dinner, 24-hour teas and cappuccinos, and complimentary internet.
As Alexandra pointed out there can be differences of your experience within the same cruise line depending which ship you pick. I went on the new Uniworld River Antoinette last December and absolutely loved the upscale decor, the new amenities of an indoor pool spa, small movie theatre, and self-laundry. However; the older Uniworld River Princess was not as impressive to me. The newer ships with Avalon like the Luminary and Panarama, also have newer features and amenities. Most of the newer river ships of Uniworld, AMA, Avalon, and Viking, are boasting the ceiling to floor windows, actual balconies with sitting area instead of just French balcony, and added features of pools, whirlpools, Al Fresca dining.
River Cruising has been exploding and the cruise lines are adding new features and amenities just as the ocean cruises have done over the years.
Personally, for me I pick the itinerary and date first, and price. If it happens to be on a newer ship with more amenities, than that's great. But if it happens to be on an older ship thats ok too.