I've had numerous examples of both guns over the years. The two designs are completely different in feel, balance, handling...they're both falling block single shots and yet IMHO they couldn't be more distinct from one another. I've pared down my gun collection drastically lately, and have kept one of each. I love using them; both of them are the kind of gun that I look for an excuse to use. And after decades of playing with both of them...I still can't decide which I prefer!
Ruger #1's are big heavy rifles; they look sleek but compared to most Euro single shot hunters they are pigs; battle axes rather than fencing foils. For me, their stocks are well suited for scope use; I can't comfortably use their iron sights. They fit me fairly poorly and transmit recoil to me worse than almost any other rifle style. If it sounds like I don't like them, well, I don't in a lot of ways...but I still think they are about the most gorgeous standard-production rifles made and the one I have is among the last guns I will ever sell. I read a lot about how these rifles tend to have accuracy problems; I've never experienced that. All mine have been good to excellent shooters, with only a few needing some minor tweaks or extensive load development.
1885's may or may not weigh less than #1's, but for whatever reason they feel lighter, at least to me. Different versions of the 1885 design can be had from several makers, with different stock styles that can be suited for open sights, aperture sights or optics. I prefer them with iron sights, specifically hunting-oriented aperture sights, but I've had a couple that were scoped and worked very well. In particular, a Winchester Safari version in .375H&H, wearing a scope, is one of the dozen or so rifles out of many I've owned that I most regret trading away. As stated above, the ability to decock the hammer manually is nice. An 1885 is, to me, much more recoil-friendly than a #1 in the same chambering...even when it's got a hard buttplate rather than a soft recoil pad.
Guys asking which bolt-action rifle to buy are often recommended to handle several different models to see which feels right to them. IMHO, the difference between a #1 and a 1885 is vastly greater than between a couple of different bolt guns. More than ever, handling and comparing these two before deciding which to buy is a really, really good idea.