I had a PM3350 too, but it was really limited. I think, it was their first Combi-Scope with On-Screen Display and microprocessor-controlled Controls. Earlier Scopes had complete "Analog" controls, or only very limited digital controls.
But according to the Manuals, the "facelift" (PM3365 among others) is much more sophisticated: They have advanced aquisition-modes, more measuring-options, higher analog bandwidth. And they also feature a equivalent-sampling mode. I don't know if the PM3350 had that, but I doubt it, as a 16Mhz signal looked very "Pixelated".
The User-Interface is identical though, which is a good thing. It's clean, all functions have their own buttons. No digging through menus to get the signal on screen. And every press of a button yields immediate results, unlike the DS1104Z, which seems a bit sluggish to me. Especially if it has been running for some time.