I routinely see people recommending 4K(4096x2160) over UHD (3840x2160) without any and justification other than the slightly larger horizontal resolution. Unfortunately this introduces another new aspect ratio to support, and I would maintain that supporting the new aspect ratio will require equipment investment at an unnecessary cost.
While it depends on the purpose, for compatibility's sake, 3840x2160p is a common 16:9(1.77:1) aspect-ratio standard and really should be the spec(Digital Cinema people excepted). Current HD resolutions down-scale(1920x1080 and 1280x720) uniformly due to the harmonic pixel sampling of the conversion. Coming from 4096, you have to squish it to fit on 16:9 playback, and now all your circles are ovals. If you are going to project your images, getting custom screens that are 1.89:1 are going to be a bitch, as 16:9 screens are the de-facto standard for manufacturers(Fast Fold/Stumpfl). If its for mapping or going to a 4096(1.89:1) destination, sure, but you loose all compatibility with the already existing 16:9 format infrastructure for current output devices. Until people start adopting the new wider-screen format, your nice 4096 content will have to be non-optimally downscaled and letterboxed.
Stick to 16:9 and save yourself the headache.
Image via MadCatz