I've got five Uberti 1875 pattern revolvers, which are very similar to the 1890 Police (in fact, they are identical except for the ejector rod housing -- you can convert an 1875 Outlaw into an 1890 Police by just changing the ejector rod housing and adding a lanyard ring). I use them in cowboy shooting. What I like about the Remington replicas is the grip/frame shape, trigger width/position and hammer shape. Compared to a Colt clone, the Remmie replicas have grips that extend much further rearward. This results in a longer reach from the grip to the trigger. I have always found the Colt's trigger to be much too close to the grip, so the Remington feels better in my hand. With a Colt clone and a natural grip, the trigger hits my trigger finger between the first and second joints. That makes it hard to get a straight press to the rear, so I have to concentrate, or bend my finger unnaturally, to avoid "pushing" the shot to the left. With the Remmies, the trigger falls naturally to the pad of my finger -- where it should be.
The Remmie trigger is also much wider than a Colt's, allowing easier trigger control and a more positive feel.
Finally, the Remmie's hammer spur is lower, making it much easier to reach with the strong hand thumb. This makes it easier to shoot the Remmie one-handed ("duelist" style, to use the cowboy shooting terminology). It also makes it slightly slower for two-handed shooting, so it's a trade-off.
Here's the bad news -- fit and finish tends to be pretty poor. Every 1875 or 1890 Uberti made in the last few years that I've handled (and that's a LOT) has been in need of a good action job. Uberti does a horrible job of polishing and fitting the frame and internals. Tool marks and rough surfaces are everywhere. Uberti uses the cheap way out, which is to fit heavy springs that will overcome the friction of those poorly finished and fitted parts. This results in a gun that isn't fun to shoot, isn't fast, and more importantly, tears itself up pretty quickly. The timing is also often off on out-of-the-box Ubertis, and the barrel/cylinder gap can be way out of spec. Uberti has some very loose tolerances.
The springs do need to be replaced, and there aren't many off-the-shelf options. EMF now offers a lightened mainspring for around $15, but it won't do you any good without a decent action job, anyway. Colt springs can be modified to fit, or the stock Uberti springs can be polished (to remove the tool marks that act as stress risers and cause failure) and shaved (to lighten them). Get a couple of extra hand springs from VTI Gun Parts while you're at it, because these guns eat hand springs like potato chips.
Bottom line -- I really like Remmies, and I shoot them much better than I do Colt clones. They're different enough to get a little attention and "style points", too, if such things matter to you. Just plan on spending $75-100 to have a new one worked over by a competent gunsmith. What you get back will be smooth, reliable and fun to shoot.
Any gunsmith who handles Colts and Colt clones can do a Remington replica, as they work in exactly the same way. I highly recommend Steve Young (aka Nate Kiowa Jones) of Steve's Guns:
http://www.stevesgunz.com. He does an excellent "race ready" action job for $90 that includes recutting and polishing the forcing cone for better accuracy and no leading. I've had other gunsmiths screw up these revolvers, but Steve has never let me down.