diffuser or absorption panels, which would you choose?

That’s the wrong approach. You first have to identify the problem before implementing the solution. The first step should be an analysis of the listening room. Acoustic companies offer that service. Best to contact them directly.

Is there an iPad app that I can use to evaluate my room? I have a acoustical microphone I can plug into my ipad so that's not a problem.

REW?

Check around your area to see if you can find a local builder. I found a guy via FaceBook (which I never use for such things) and he built panels and bass traps for a fraction of the cost of some of the ones you'll see offered. Granted, there's nothing wrong with those services, room correction, etc. Please don't hear me dismiss that. But I was able to build, add, and add a few more, finally with 2 diffusers for several $100 vs. thousands. And custom made, same insulation options, and I was able to get the precise sizes for my room. 

There is no such thing, you need both. Any research you do will tell you that. Wish it was that simple.