Regarding pick-pockets, a lot of it is common sense and I agree not very different from theft here in the US. Generally, the more you are in the middle of the crowd, the higher the likelihood of you getting pick-pocketed or at least someone trying to pick-pocket you. This is especially the case if you're wearing a backpack or carrying a purse. Don't get caught up in the riff-raff and with all the other lemmings at major attractions.
I almost got pick-pocketed at the Colosseum in Rome at the main platform/overlook that has a view of the Colosseum right down the middle. My wife and I were weaving our way through the crowded platform area to get to the overlook for a picture when a team of thieves went after us. One, a woman, distracted my wife by stepping in front of her and waving her phone around to fake taking a picture while blocking my wife's view of my back. This was to isolate me so my wife couldn't watch my back. I then felt a sharp tug on my back while taking pictures, stopped, and immediately swung my pack around (fortunately it was one of those photo backpacks that has zippers that aren't super-easy to unzip or zip, which worked to my advantage in this scenario). I found that the upper-compartment, which had my tablet in it, was a third of the way unzipped. I'm guessing the *tug* was either from a quick attempt to unzip OR an attempt to quickly pull the tablet out. I spotted the guy who tried lifting the tablet and he was a larger dude, probably over 6ft. Regardless, I followed him back to his group of pick-pocket friends, stared him and his friends down as we walked by and cussed him out "under my breath" but loud enough to where he could hear me and see me talking. Probably not the best idea but it was a heat of the moment thing. I immediately went over to one of the staff office locations and reported the activity in the area - I think they sent some police officers up there not long after. There was probably a group of 10-12 pick-pocketers sitting in the back by the columns watching the platform area - the M.O. was probably to pair of in twos or threes and go after unsuspecting tourists who are crowded like sardines. I'm sure it's easy-pickings in situations like this.
So wherever you are, whether it's on a crowded train, Metro station, popular attraction, or any small space, always be aware of your surroundings and avoid getting yourself into situations like the one I foolishly got myself into.
As far as money belts, I've typically carried one wherever I've travelled in Europe but I would say it probably isn't necessary if you practice common sense. That said, I'd rather have my passport as close to me as possible and not in my bag, so a money belt is nice for that. I would avoid the leg ones (some dude frisked my dad's leg as we were getting onto a train from the airport which was scary). The best ones, IMHO, are the money waist packs. Nobody will try to frisk you there and if they do, at least with me, they'd get a knee in the groin and or face.
If you carry a wallet in your pocket, try to keep it small and on a leash if possible. There was another incident/close-call while I was on a train, and some random kid sat next to me and started striking up conversation. I had my jacket in between us and I think he was trying to distract and see if he could slip my wallet out. When I picked my jacket up, sure enough, my wallet was sitting right there... still not quite sure how he even got that far but some of these guys are crazy-good. If someone (especially a shady-looking local youngster) tries to get all chatty and friendly with you, especially at a train station or on the train, back-off and increase situational awareness - chances are that they aren't just trying to be your friend but are potentially trying to distract you to pick-pocket you. Seeing that you're traveling with a group, it shouldn't be that bad though. I think most people are prone to this when they're alone or separated - again, this goes back to the M.O. that pick-pocketers operate under where usually the first couple steps are to isolate and distract, in no particular order.