Again, the first question, "What are you planning to use it for?" is necessary for any adequate response. I reload and have both a 24" rifle and 20" carbine in 357mag and find that I can load 38spl+P cartridges and still have plenty of juice to shoot over 200yds at the range. My 357mag loads make shooting 300yds actually much easier than I thought it would. BTW, my Hodgdon's 2002 handloading manual shows loads for 18.5" rifles while their newer versions don't.
Handloads.co's ballistic calculator shows that a hot 158grn 357mag and a hot 240grn 44mag both have similar trajectories out to 300yds so for range work it's a tossup on which one you'd want to use. The 357 mag uses a lighter bullet and less powder so it's cheaper to reload (but the difference may be minimal if you cast your own bullets). The real difference between the two calibers is muzzle energy down range.
It calculates that on an 65° at 6,100ft elevation where I live, a 158grn .357mag with a velocity at the muzzle of 1,822fps, maintains 1,476fps and 764lb/ft of ME at 100yds, 1,211fps and 515lb/ft of ME at 200yds, and 1,044fps and 382lb/ft of ME at 300yds while a 240grn 44mag with a velocity at the muzzle of 1,817fps maintains 1,491fps and 1,185lb/ft of ME at 100yds, 1,236fps and 814lb/ft of ME at 200yds, and 1,067fps and 607lb/ft of ME at 300yds.
Of note, my 38spl+P loads are about 60fps slower out of the 24" barrel vs the 20" one while my 357mag loads are 10fps faster in the 24" barrel. That means that the lighter powder charges are running out of gas in the longer barrel and slowing down before they leave the muzzle. I'll assume that the same would be true between 44spl+P and 44mag but I've not demonstrated that.
I use both my 357s for range shooting where all I'm doing is trying to ring a steel plate so I don't need a 44mag as my 357s are cheaper to reload. If you're going to use one for hunting and you recognize the limitations of a pistol round, even in a longer barrel, then I suggest that you go for the 44mag.