Several reasons the army caliber is better in my opinion.
The main one is finding a good assortment of round ball.
Locally, or even on the net I generally only see .375 for the 36. You can find .380 on the net, or get a .380 mold (which I did), but for the 44 it is much easier to find .451, .454 and even .457.
this gives you better options to tailor the ammo to your gun to make sure balls neither jump forward, nor are too difficult to load.
The bigger hole of the 44 makes target shooting a bit easier as far as being able to see where you hit.
Accuracy can be made a bit better as there is more room for powder (or powder and filler) which can allow for light loads or hunting loads with a broader range than the .36...again you can tailor it to your needs better.
The main advantage of the .36 IMHO is the slightly reduced amount of lead
Don't get me wrong I really do like my Navy, but I tend to take the .44 more often.
Recoil isn't all that different one to the other, nor really is the amount of powder used...some difference of course, but it's not like you will be burning tons compared to a .36.
On the other subject, I will say my Peitta navy .44 brass framed sheriff certainly did not come out of the box high quality. It took a decent amount of work to make it a nice gun that I do really enjoy. At the price I got it ($120), I would certainly do it again...I do enjoy the working on them though, so I wouldn't in good conscience recommend them to someone unwilling (or unable) to put some time into it.
I have looked at their Remingtons (steel frame) and plan to get one, they do seem high quality in the store (local cabelas), I haven't had a chance to hold one of their steel frame colts