I tested this topic myself in practice because I worked with a guy in the dorm who had two fridges - an old Biryusa and one with NoFrost. There really is a difference, but it's not that the fridge doesn't need any maintenance at all. The system works like this: the compressor periodically defrosts the evaporator automatically, moisture drains into a pan and evaporates. Sounds nice, but in practice you still need to clean that pan sometimes, and if something clogs it - you can have problems. Plus this kind of fridge uses a bit more electricity because of the system running.
But honestly, I'd still switch to NoFrost. The thing is not that defrosting is completely eliminated, but that you can do it once every couple of years instead of regularly dealing with ice buildup. Plus you don't have to turn the fridge off for like 12 hours while the thawed water drains - that convenience is worth the extra cost. If you've got an old Biryusa and you're always messing with it, then a NoFrost model will pay for itself just by getting rid of that hassle. But if you don't bother with defrosting and your fridge is good enough - I don't see the point in paying twice as much.