Dessert Eagle? Does it have Cool Whip or something?
There are several Desert Eagles in my family. My dad and my grandpa each had older Mk VII .44 Mags, and my brother bought a Mk XIX in .50 AE when he got home from his first tour in Iraq.
Good? They are well made. Quality of materials, machining, and finishing has been very good on every Desert Eagle I have handled or shot. They are rail gun accurate. They have a fixed barrel and their gas operation and rotating bolt means there is nothing moving forward of the bullet until it leaves the muzzle. I have seen my dad hit a rock the size of a laptop on a hillside a laser ranged 200 yards away 6 out of 8 times from the supported offhand position. They are fun. Chopping firewood with 350 gr JSP from my brother's .50 AE is almost the most fun I have ever had with a gun. The fireball is visible in the daylight. The thing is a beast. We are a country of over indulgence, and the Desert Eagle fits very well into a lifestyle of Super Sized value meals and 1000 horsepower sports cars. And they are generally reliable. With a caveat. You have to manhandle the things. If you limp wrist or allow it to pull you around, it will short-stroke or hang up on you. That is just a compromise you make with automatics in general. They aren't going to be as forgiving of poor posture or weak technique.
The bad. Well, they are big. If you have small hands, it might be hard for you to get enough of a grip on it to really control it. And this can lead to issues. Its weight helps control recoil, but makes it difficult to pack. I know latest versions have addressed weight issues and added a compensator, but it is still a handful. This is both part of the appeal of the design, and kind of a bummer. Speaking of recoil, the .44 is soft shooting, but the .50 has some recoil, and more than that, it is a unique type of recoil. The rotating bolt means that instead of coming straight back, the pistol tends to torque in your hand. This can lead to brass being ejected straight back in your face, and it takes some getting used to. If you have thin little bird wrists like me, I don't want to say it is painful, but after a few mags, it can be fatiguing. Ammo is expensive for the .50 AE, so you will want to reload (which means keeping track of your brass, which might be difficult in some of the country you hunt in). And you won't have the ammo choices regardless of caliber, because the gas operation means you can only shoot jacketed ammunition, and the feed ramp profile means some of the bigger meplats or longer bullets aren't going to function well. And finally, this one is more subjective, but I think the controls suck. As an American, I believe in the spirit of John Moses Browning (Blessed are thee among inventors...) that if a pistol has a safety, it should be frame mounted and down swept. The up swept, slide mounted safety seems to be the worst possible design in the worst possible place. And the size of the pistol means reaching it is almost impossible in the firing grip, so the Desert Eagle becomes a handgun that requires both hands to operate (handsgun?).
Overall, I recommend never passing up an opportunity to shoot one, but I don't know if I personally would ever spend money on one. They just don't seem that practical to me. Fun, yes. But not very useful.