I own both the iPad 2 and the Transformer Prime... so let me break this down just a bit.
1. iPad 2 (or in your case, the iPad 3). Frankly, it just works and works well. My entire family has either iPhones or iPod Touches and these days, with Photostream and iCloud, using these devices in tandem is completely effortless. MOST every task I'd wish to perform on these devices is extremely intuitive. But some small things here or there make their use frustrating. For instance, if you find a pic you like on the web and you want to copy it's web address, it's NOT straight forward at all. Just one example out of a few. My iPad 2 was very well constructed, had held the test of time with four boys in the house, and has even been there in most of my musical composition in the last8-9 months, above and beyond my PC (and I use ProTools, you'd think that'd be hard to compete against!)
2. Transformer Prime: Just got this a few days ago. I'm impressed! First off, I love the keyboard. I've sold myself on getting a bluetooth keyboard for my iPad (I have no idea why I haven't done so before now...) because of the Prime. It's fast, versatile, and does a few things the iPad cannot currently do (once again, just small things, but things you tend to miss when moving back to the iPad). HOWEVER!! TP's ver. of Android (which all Android devices feels this way to me) is not exactly intuitive or "natural" feeling. I really had to figure out the right way to do certain tasks... too many button presses for a single task that should just take one. Most people who are used to Android devices would feel right at home. It's still taking me a bit to get used to it.
I'd write some specifics, but I've gotta jet. Do some reading on sites like Newegg (customer reviews) and TechReport (professional reviews) to get a better feel of which device might suit you best.