As far as asking which is better previcox or rimadyl, that in a lot of cases could be a matter of opinion. Previcox is one of the newer "NSAIDS" (non-steroidal anti-inflamatory drug) to come onto the market. Its primary benefit is that it is more selective on a specific type of receptor (COX2) that is responsible for pain. Rimadyl isn't as specific and effects both COX2 and COX1.
Here is the Previcox home page if you want to immerse yourself in the information on the product.
Previcox can also have liver side effects like Rimadyl can. At this point, I don't know how high your dogs liver values were, but I would say that your vet has set up a decent plan to recheck those values. You could always ask to recheck sooner to see if they are getting better or not. If she's been doing well on the current dose of Rimadyl, could you start to taper the dose to the lowest level to effect. If doing every day, would every other day work? As far as switching to Previcox, that might have a benefit of decreasing the liver values, and it might not. Time would be the tell tale factor there.
Some other things to consider in arthritic dogs that might help out. Glucosamine and chondroitin sulfate supplementation can help to promote better joint health. Some dogs have marked improvement on it, some don't. A product called dasaquin is also used in many clinics to help with arthritis. I'm sure your vet would encourage conversation about their experience with both of these.
I would talk with your vet again about your concerns and see what he/she has to say. If you want to make the switch, I'm sure they wouldn't have a problem.
Hope you can keep your little girl comfortable for a very long time!