My DE experience
has been with a .44 mag Mark VII, six inch barrel, alloy frame, over the last two years, shooting almost every week. Its been a real love-hate relationship for me.
Its too big, but then again most guns are because I have small hands. I put a Hogue rubber grip on it, without which I would not be able to keep a firm grip. Like anything else, you get used to it.
The recoil is strong, but not as strong as a large .44 mag revolver. The action of the gas operating slide absorbs much of the kick. Again, once you get used to the recoil, it is not really an issue.
It has remained the most accurate handgun I own, much more accurate than I am capable of shooting. I can actually hit targets at 100 yards, which for me, considering my eyesight, is outstanding. Note that I did not say how big those targets are. I have noticed no degradation in accuracy over two years, and probably over 2500 rounds fired.
You've got to keep the thing clean! If you seriously dislike cleaning guns, do not buy a DE! I cannot get over 50 rounds through it without a thorough cleaning. Clean in accordance with the website indicated above. If you do not, the slide may freeze up and you'll have a hellava time trying to get it unstuck.
Initial cost is high. But as indicated by others above, I believe I could get most of my money back out of it if I wanted. So I do not see cost as a real issue. Cost of ammo: I reload, anybody who shoots several times a month needs to reload otherwise you are waisting $. Not an issue if you are very well to-do. I've found standard 240 grain semi jacketed soft points to shoot the best. I like AA#9, BlueDot, and VV105, loaded slightly under max.
The trigger is wierd, a little heavy, and has a click to it, once again, you get used to it.
The worst problem I have had with the gun is its failure to extract the spent case. I thought I had the problem solved by installing new springs. That reduced the problem greatly, but not completely. It still jams up on me about once every 25 rounds. The DE must be very firmly held, the slightest limp wristing will likely cause it to jam. The jamming problem is the one thing I have considerable difficulty in dealing with and has almost caused me to trade the gun. But what would I trade it for? I love the feel of the power of shooting a .44 mag semi-auto.
I have no experience with the .50 AE.
I hope some of the above discussion helps. The problem here is my experience of course is limited to a sample group of one gun. You may get one that never jams, or maybe the jamming problem has been corrected with the newer Mark XIX. Who knows? I'd sure like to hear if it has.
One more thing, if you like being politically incorrect, as I do, get a black Desert Eagle tee shirt. It has a small Magnum Research logo on the front and a large image of the gun on the back. Be cool, wear it to the church picnic. My sons love it, its one shirt of mine I won't let them wear. Best of luck.
) like Glocks, and you want to use a flaky gun like the Desert Eagle for home defense? No, incidentally, the Desert Eagle is not worth the price, or even a respectable fraction of it. The Baby Eagles aren't too bad, but of the three CZ-pattern brands I've owned, they're my least-favorite. 
The MK XIX uses the .50AE frame for all calibers, so with just one frame you can have all the cake you want.