The general difference between vintage and modern is primarily in the area of shell construction and QC: vintage drums tend to be thinner (and lighter), and were formed in a heat mold that used some sort of pressure upon the plies whereas modern drums tend to the thicker and the shells are often made in vacuum molds, these differences translate into a "stronger" shell that tends to a bit louder and more tune-able (in certain applications), and as for QC, a ,lot of "Monday morning" kits made their way out the factory and into the homes of many players.
There are, of course, exceptions to both shell construction and QC among certain brands, as no doubt some may come away after playing a "vintage" Rogers kit feeling as if they'd just played a modern kit, which, apart from the hardware, it kind of is (i.e., bearing edges that are at outside edge of the shell as opposed to the middle, five-ply construction, etc.).
Most vintage bass drums can be kept in their place by using a modern pedal that has Velcro at the bottom and/or cleats that keep it from creeping. Tom mounts are another thing, If you're a one-up, one-down player, then most single mounts are adequate; if not, there's the snare stand option. If you're a two-on-top player, then the Ludwig, Rogers Swivo, Premier, and Sonor Champion-era double tom mounts are good options, while the Slingerland double Set-O-Matic as well as that Gretsch SS-era mount are both quite dreadful.