In general, higher voltage means more torque in a motor, and therefore more oomph to do stuff.
So my 14" Ryobi 18V cordless chainsaw will trim a branch or two, but a 80V saw will handle it a lot quicker, and will also power through a log up to what's reasonable for its 18" bar, where my 18V Ryobi would get hopelessly bogged down, or take for ever in comparison.
Oversimplifying, I think your battery Wh (=Ah x voltage) will determine the total amount of cutting (aggregate area in sq in) you can get done on a single charge, while the voltage will determine the ambitiousness of what you can tackle, and how long it will take you to cut it.
Of course, it depends on more than just voltage, and I'm sure a modern DeWalt 20V will beat my crappy old Ryobi 18V by quite a bit. However, it's only been with 40V and higher voltages that people who use gas chainsaws regularly have started saying, "hey, this behaves like a real chainsaw, not a toy". And the 56-80V offerings generally get better reviews than the 36-40V ones.
From what I've understood (reading) and been told (by pros and would-be pros), for full coverage you now do best to invest in 2 ecosystems. 18-20V for hand power tools, and ~60V+ for outdoor power equipment (chainsaws, mowers, etc.) I'm not too familiar with DeWalt (around here it's pretty price premium in general, and very much so, if available at all, for outdoor power equipment like chainsaws and trimmers), but if you're with them I would explore if you can go for their new 60V/20V Flexvolt line. You'd probably get a lot more saw with their 60V brushless, and -- hopefully, please check! -- the batteries would be backwards compatible with your 20V system though I doubt your old batteries would work in the saw. But if a 12" bar to trim the occasional branch or cut off a 4x4 post is all you need, then yes it will be overkill.