My V4 is small and in an acrylic case while the V1200-powered A1200 next to it is much bigger and beige.
OK, now seriously: the V4 on the one hand and V2-equipped Amigas on the other mostly differ from each other in that the V4 has a not-yet-perfect AGA reimplementation while the original AGA is, of course, perfect AGA. If you want to run old Amiga software, the V4 can only approximate an original Amiga's compatibility. The V4 is more of a work-in-progress than the V2 series of Vampires because the CPU part both have in common is pretty much complete and work now concentrates on the chipset reimplementation in the V4.
On the plus side the V4 has 16 (?) MB of chipmem available even to old applications while AGA generally is capped at 2MB. The V4 is not slowed down by chipmem (its "chipmem" reaches hundreds of MB/s speed). The V4 has 512MB of RAM while the V2 comes with 128MB. Both is plenty for most Amiga uses (I used to have 8MB on my Blizzard 1230 which also was a lot in ~1995).
All Vampires are very, very fast for Amiga-standards (but obviously very, very slow for 2021 PC-standards). They are faster than any overclocked 060-equipped system. It depends on what you are going to use your Amiga for whether this comes as a pro or con. If you only want to play old games that ran well on an unexpanded A500 or A1200, the speed is often more of a problem than helpful as it may lead to all sorts of unwanted side effects in games that were coded when nobody imagined CPUs in the 100s MHz speed range. If you want to run a highres Workbench from harddisk (or rather CF card), 060 AGA and RTG demos, some ports of PC games such as Doom, Quake or Diablo, then the Vampires are a very good choice.
The Vampires do not have a 68k-compatible MMU if you are into coding and debugging on the target machine.
The V4 has some extensions to the graphics and sound chipset like 16bit audio, extended sprites, copper in chunky displays and probably more I forgot. These extensions may or may not be used by new software. The custom chips in the A1200, of course, remain unaltered by the V1200 although there are plans to port back the enhanced chipset functionality from the V4 once that is complete.
Personally I like the V1200-A1200 better than the V4 because it is my original Amiga with a very powerful accelerator including graphics card functionality. It looks and even smells like an Amiga. The V4 does get a lot of use though since my children use it to play Amiga games (when I let them).
Please do that work on your A1200 or give it to somebody who will do that work regardless of your purchase decision. The number of Amigas in working condition can only get lower and if you do not recap it, it will inevitably die a cruel death eaten by leaking acid.