I have a Canon compact camera and a Nikon DSLR. I like using both of them. The Canon's menu is easier, but I like my Nikon best because I want to be able to manually select all settings. My Nikon allows me to do that in an easier way, probably because I know all its ins and outs. 
As CG stated, it all depends on whether your wife wants to have a small camera that is easy to take wherever you go, or go for a bigger camera with multiple lenses. It goed without saying that the amount of money you want to spend on a camera plays a roll in that too. These days there are so many excellent compact cameras out there and at great prices too! But then again, DSLR's are relatively cheap too nowadays.
Whatever you select, I would recommend her doing a photography course. Not until when I did a beginners course, a few years ago, I used my DSLR mostly on "automatic". Such a course will give you insight of how to use the different settings of the camera and photography in general. Things like composition, depth of field (DOF), focus, white balance etc. etc. are discussed. A course like that is well worth the money.
Good luck, and let us know what you bought her... 
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