If you can, try it out on the 4K TV before making any decisions, it may work for you, in which case you'll have saved a fair amount of cash.
On the other hand, if it doesn't work as well as you hope, you'll at lease get to see the image quality 4K has to offer and whether or not you like having a 4K desktop.
4K.
For: Higher resolution gives pin sharp images, not only in games but you can also now stream super high rez movies and YouTube content.
Against: Some issues with Win 10 scaling of the GUI. With a 'mere' GTX 1080 you'll need to lower some game settings to keep the frame rate up. Older games can look terrible. You're stuck at 600FPS no matter what.
1440/144Hz.
For: Super fluid gameplay in many (but not all games, a few are so demanding even a GTX1080 will struggle to keep them over 60FPS). No scaling issues with the GUI. Older games don't look quite so bad.
Against: Cost, these faster displays are often more expensive than same sized 4K monitors. Lower rez limits playback quality of movies and digital content.
It really depends on where your priorities lay and only you know that.