Is the Deramaxx a lot like aspirin?
No it's a little like, not a lot.

Both Aspirin and Deramaxx will inhibit the enzymes Cox-1 and Cox-2. Aspirin does so in about a 50/50 ratio. Deramaxx being classified as a Cox-2 inhibitor will inhibit the Cox-2 enzyme magnitudes of order over the Cox-1 enzyme. In another words it will inhibit the Cox-1 enzyme very weakly, whereas aspirin will inhibit the Cox-2 enzyme relatively weakly.

The Cox-1 enzyme is needed for production of the prostaglandins hormones, which is a carrier signal of pain to the brain. Another primary function of the prostaglandins is to maintain the protective coating and secretions of the stomach lining. Inhibit the protaglandins with aspirin the pain signal is blocked, and you end up with stomach irritation and possibly ulcers in dogs.

The Cox-2 inhibitors inhibit the Cox-2 enzyme which is directly responsible for inflammation and the sensation of pain. In theory they should not be as irritating to the stomach. But sometimes their weak Cox-1 inhibition can lead to problems. Their main problem in dogs is the effect on the liver.

You should ask your Vet to start running liver profiles every 3 months. It may be your dog will never have problems with rimadyl. But then again if it does hit the liver, it can cause severe problems very quickly. It's a case of better to know before hand.