I can confirm that the dx12 patch does wonders for lower end CPU's.
I'm running an ancient
[email protected] (yeah I'm actually still running this thing and it performs surprisingly well in modern games), paired with an 8Gig RX480. I'm used to turning down stuff that chokes my CPU. In The Division dx11, this seemed to mainly be streaming distance and, to a lesser extend, object detail. I got similar fps as the OP before the patch, with noticeable slowdowns in the bigger open areas and/or with a lot of action going on. This was with streaming distance/object detail turned down to around 60%/80%. All my other settings were maxed out including Nvidia PCSS, except post FX AA was set to SMAA*1 (low). My GPU temp never got above 74C.
Now, with dx12, the game mostly runs at around 40-60fps (limited at 60fps) with only the tiniest of perceptible slowdowns when there's lots of action on screen or in big open areas. On top of that, this is with maxed out streaming distance and object detail. I didn't think dx11 performance was bad, but dx12 absolutely crushes dx11 on my rig and makes me feel as if my GPU is finally free of any CPU bottleneck, the difference is absolutely huge. I think this is amazing, given I'm running this game on an almost 9yo quad core dinosaur. I also noticed my GPU temperature went from 74C to 77C, indicating that my GPU is actually stressed for once (I rarely see temps above 74C in most games and I'm always running GPU-z in the background to watch temps). The only thing I noticed was some weird, momentarily, geometry glitch, always happening at the same spot but this was nothing game breaking.
TL;DR After testing for a few hours, I'm very happy with this update and I wish more games would come out with a dx12 patch like this one. It allows your GPU to fly if you're still rocking an older Quad core CPU like mine or apparently an i3 as the OP.