I personally prefer DSR, but it's mostly more practical reasons than visual reasons.
Main reasons are:
1) 4k native does not have higher than 60hz monitors, but you can DSR a 4k on a monitor with higher refresh.
2) 4k monitor costs about as much as a high quality 1440p 144hz monitor, though it's getting cheaper, so I could be wrong on that.
3) 4k would look pixelated as soon as you drop down its resolution, with DSR 4k on a lower screen, you can drop resolution some and compensate with smoothing if your resolution is still above your screen's native, and at very least you'll have your lower native to keep the screen from being pixelated.
4) You'll need a displayport for 4k monitor, which not every GPU has, although most modern ones do, so you may also need to upgrade your GPU, which adds to the expense.
I'd say try DSR 4k first, if you like the fake DSR 4k enough, the real one would probably look better.