I will preface by saying I am not an expert... I have never used Dura-Ace or 105.
However, from my understanding the major benefit of the upgrade is that you will save a couple of grams on bicycle weight... and of course the bling factor! Of course if you are replacing a new 105 with an older Dura-Ace, then you might just have bling.
The pieces should be interchangeable, but the alignment and adjustment may make it enough of a pain to bypass the process if you aren't sure about what you are doing... of course books, the Sheldon Brown site, and the Park Tools site will give you details on how to adjust the equipment if you want to take that plunge.
If the derailleur happens to be adjusted properly and the alignment of the hanger is not different between the two models, and you install it properly, it is just swap it and ride... but that is best case. I would expect you will need to do some adjustment as well.
A friend gave me a spare (long story) Dura Ace rear derailleur. My bike is equipped with 105. Can I put it on (or have it installed) Is it worth it to do, are there any real benifits to it?
If it's Dura-Ace designed for 8-speed or previous, then it's got a different amount of cable pull and will not work with current Shimano 8/9/10 indexing. If it's 9-speed Dura-Ace (I highly doubt your friend gave you a 10-speed!) then it'll work fine.
Yeah, I'd just save it for a project. There'll be very little to absolutely no discernable improvement in performance, although you'd save 50 grams or something like that (if you're counting, there are 454 grams in pound).
I haven't used 105. One day I'll build a bike with it. If blind testing were safe on bicycles, I'd bet nobody could tell a current Ultegra from a current DA drive train in actual use under such a test. I suspect it might be the same with 105. One cay I'll find out.