All three can cause stomach ulceration.

Mobic and Ibuprofen are not Cox-2 specialists.

Celebrex mainly works on Cox-2 (inflammation) but has some weak Cox-1 effects (stomach ulcer potential).

Mobic is chemically related to piroxicam (which was one of the more toxic NSAIDs.) Its brand name was Feldene. It fell into disfavor because of the severe reactions some people had to it.

Some doctors remain confused about Mobic thinking it is like the Cox-2 inhibitors, because it came out at the same time period.
But it is NOT sparing of the stomach potential for ulcers, and it has the same cardiovascular warnings with it.

All the NSAIDs have potential for causing heart attacks, because they block a beneficial Cox-2 cytokine called prostacyclin. The one less dangerous to the heart is naproxen (OTC Aleve). I use the Aleve liquigels now when I need some pain relief, and I have found the liquigel form very fast acting and stronger than the pills. I think you can get by with much less with them. Only one a day will last me all day and work on mild to moderate pain for me.

I use Salonpas patches more often than I take pills. They work on my pain issues locally and are safer.

Using a quality antioxidant like grapeseed extract (200mg a day) can really help with chronic arthritis and allergies I have found.