It's quite common if you don't do one of three things about it.
You can either put the fixed pin mod in place, you can fill in the notch in the hammer with a good epoxy or you can just roll the gun strongly to the right while cocking the hammer.
Apparently being a lazy sort I have not got around to trying either of the first two idea yet. But I do rely on the third to greatly decrease, if not quite eliminate the issue. The last time I shot my pair of 1860's in a cowboy match I got shards down inside once or twice despite rolling the gun as I cocked it. But I only once had to use my other hand to aid in turning the cylinder into place as I cocked the hammer. It didn't totally lock up and it continued to finish off the shots just fine.
There's also another great reason to roll the gun. If you don't you risk having hot cap shards fall between the grip and your palm. And they ARE HOT ! ! ! ! After a match I often have a red spot or small blister to show for the times I didn't roll the gun far enough....
The "classic" way to avoid this is to point it literlly at the sky or even slightly past vertical so the shards fall clear of the hammer. This method being the one used by the old cavalry officers that primarily used a pistol and sword instead of a rifle. But most ranges don't let us shoot from horse back and don't like to see us pointing a cocked gun ready to fire at that sort of elevation and then bring it back down to fire. So rolling it to the side is about all we're left with.
When I mess up the roll and cocking and get a hot cap landing on my palm it's also one of those times I wish I were a leftie....
As for pin vs filling in I've seen just about 50-50 proponents of each method. Each claims to all but totally eliminate the problem. Of the two filling in the hammer is easier and the epoxy can be easily dug out to give room for the pin if the filling in idea doesn't cut it.
I've got a pair of Uberti Remingtons as well. While MUCH better on this issue they are far from immune to being jammed with cap shards. The difference is that the bits that get into the hammer area tend to be smaller so they don't quite lock it up totally.
Which do I prefer? Having shot each pair a few times in both larger cowboy matches as well as our monthly fun matches and even a few plinking and general sighting in sessions I'd call my preference a wash. I like both for what they are. And I find that I enjoy both pretty evenly.
I would have to admit that the Remington pattern is both stronger, stays in alignment better and could be regarded as a technically superior design. But there's something about the open top that is so different that I like it equally either for or in spite of the "warts".
I do know that if things got tight and I had to sell one set or the other I'd have a devil of a time figuring out which pair to part with.
And no, shooting one style then the other as a mixed pair in a cowboy match is not a great idea. Different sights and a different feel for the reach to the trigger says "no".
But if you'll be buying them more for fun and smoking then the answer is an obvious "both please". It's just a matter of which do you get first....
Be aware that the Colt open tops from Italy come with some built in issues. Namely the front sight being overly low so the guns shoot very high and the fit of the arbor in the barrel for setting the cylinder gap. Read about what I did about these in my replies to bobdbldr in this other thread.
http://www.canadiangunnutz.com/forum/showthread.php/1416979-Starter-kit-for-BP-revolver
For an 1860 of course the front sight issue is a bit different due to it being a blade sight. The sight is press fitted into a woodruffe key slot so I knocked the old sight out and made up a new sight which was taller. A few sessions at the range with a small fine cut file to shorten the over height down until the POA matched the POI at 15 yards then some rounding out for the proper sort of shape and some touch up blue and the guns are great shooters.
In fact my older Uberti and even older Navy Arms .44Cal 1860's shoot as well for me as I can manage with my modern S&W's. I'm not in any danger of getting on the next Olympic team but I've been told by more than a few regular shooters that they wish they were as good as me. So the guns are certainly good shooters.
Ah heck. Here's a couple of pictures of what I did for the front sight. Coupled with the button or some other shimming of the arbor and an 1860 can be brought right up to snuff.
This first one is the new taller sight resting on the barrel and ready to go into the round bottomed slot. the old short sight is up above on the towel.
This is the jig I used to file the upper exposed sides of the blade at a slight angle both tapering upwards and thinner towards the front so the only thing you see is the rear edge. It's also in keeping with the shaping of the original.
As far as cleaning goes I don't find either is any easier than the other. The only difference is that the Remington needs cleaning from the muzzle end and the colt can be cleaned from the forcing cone end. Other than that it really is 6 of one and half a dozen of the other.
That's for short cleanings. About every three times out I do a full strip down and clean out the action. For that the Remington gets a slight nod of the head due to less screws to be removed. The Colt needs the whole grip frame broken down and that's 9 screws (5 grip frame screws, main spring screw and three action screws) where the Remington has five (trigger guard, grip screw, mainspring tension and two action screws). But even that's not a whole lot of a big deal in the grand scheme of things.