Seems like you need to find someone who's owned and/or shot both a 44mag and a 50AE mag reasearch handgun to offer a qualified answer to part of your question.
I have not owned a Desert Eagle, although I've shot a few of them -- just not enough to properly compare the two different calibers on that action for you here.
I'd look in the reloading manuals to see what chambering offers more possible energy, my hunch is that 50ae will top the 44

I do know that with the mag research autoloaders, especially the 50ae, you need to run a fairly hot load to operate the action. At a certian level, light loads just won't cycle the bolt with the big 50ae action. The way that works with this answer is that typically you can load different calibers and cartridges to get you the same recoil. Light bullets in the big caliber/heavy bullets in the smaller caliber, move velocity with the smaller caliber/less velocity with the bigger caliber, etc...
With the gun you speak of, there's the issue of *what will make the gun operate properly* thrown in to the issue.

With as much cult following as there is with the Desert Eagle pistols, you should be able to find a forum somewhere on the world wide web that's crowded with Mag Reasearch enthusiasts who can answer this question in much more of a qualified fashion.

--Tinker