There's probably NO advantage for your monitor. In your case, DP and DVI would likely be EXACTLY the same.
*If there WAS an advantage, it would be with DP likely and since otherwise DVI is identical I can't think of a reason to use DVI over DP.
Input lag has more to do with the SCALER and Video Processor (if any) inside the monitor though I suppose the DP signal may be more efficient and thus decode faster. The reason why many HDTV's have a "GAME" option for HDMI inputs as it disable the video processor to minimize input lag.
For scaling, I actually set my Video Control Panel so that scaling is done right on the video card itself:
a) Scale on GPU
b) Scale by Aspect
Or similar names. I have my monitor settings (on the monitor itself) so it does not scale (1:1). What happens then is if I game at say, 1600x1200 my video card scales this properly and outputs a 2560x1440 signal at all times (or whatever your monitor max ratio is), thus no scaling need be done on the monitor itself.
A modern video card should be faster at scaling than all/most monitors.
Summary:
- DP vs DVI probably makes little difference (especially if already scaling on video card)
- recommend scaling on video card