Then throw the old drive in the enclosure and either use it on an XB1 or Wii U or just as extra storage for your PC.
I can't believe I didn't think of this. I jumped up to a 2TB drive when I got a PS4 Pro, and about 2 weeks later I bought a 2TB drive for the Xbox One.
Speaking of which, my god, I swear the Xbox's 500 GB drive is somehow about 1/4th the size of the PS4's 500 GB drive. I'd been using the stock drives since launch, and even though I use the PS4 for every non-exclusive game, it's the damn Xbox that's always full. Right now, literally all I have on it is Halo 5 , Halo: MCC, and just a couple of Rare Replay games (because of earlier space issues), and it didn't have enough space for Gears 4's 21 GB patch. That's when I caved and got the external drive.
Meanwhile, the PS4 always had several disc games installed, and all my download-only ones as well, and I think I've only had to clear space twice since launch.