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How many people are going to answer in this thread that actually own and shoot both guns asked about?

I do.

The OP asked which one is a better weapon. That gives me the impression the OP is totally in the dark on BOTH guns. Neither one is a good weapon, from the standpoint of a combat weapon, compared to dozens of other handguns in several different calibers. Forget the Hollywood BS and forget your video game. The only thing those have in common with reality are the names and the image of the handguns.

Both are fine handguns, for sport & target uses, and each has advantages over the other.

The Desert Eagle holds 8 in the mag. It is a huge, heavy handgun (4.25lbs empty!). In stock configuration it does not have adjustable sights. Its trigger is fair. Its grip size is extremely large, and if your hand is smaller than a size 9 glove, you won't get a really good grip. It must be fed jacketed bullets, and like nearly all autos, they must be in a certain power range, or the gun will not cycle properly.

They are very accurate, IF the shooter can handle them well. Felt Recoil is very low for caliber, mostly because the gun weighs so much.

The S&W M29 a classic, the original .44 Magnum. Adjustable sights standard, very good trigger (plus the DA function, if thats important to you). Accurate, more so than most shooters. Not comfortable to shoot with full magnum loads. Painful with original factory stocks. very pleasant with reduced loads. Holds 6.

As to a weapon, if I had to use one for combat, I would choose the Desert Eagle, accepting the huge size and weight (but not happily) for the higher capacity, rapid reload, and faster recovery time between shots over the M29 revolver. If I were choosing one to defend myself with (NOT actively seeking combat with an enemy) I would pick the S&W.

But by choice, I would not choose either one for a combat weapon. I'll leave that to movie actors and video gamers.