Better? Hhhm, that's subjective.
Ballistic wise I would say the .280 Rem. as it's the ballistic twin of the .270 Win., same case as the .25-06, does have the capability to use heavier bullets when compared with the .25-06.
In years past, the .25-06 bullet selection stopped at 120gn and the .280 started at 120gn. I don't currently and never have owned a .280, but if I did I would probably use the 150gn for deer and vermin. Just seems like the place to be with that one.
The .25-06 I do currently own and it is a flat shooting round but has its limitations. I killed a heavy bodied 6-pt this year with it between 300-350yds. I couldn't ask for better performance. The 115gn Berger VLD punched through both shoulders and left a .50 cent piece size hole on its departure. Looked like a scene off the Hunting Channel. The buck made a 50yd mad dash but it was all for naught.
I shot this same load (54.0gn/RL22/BR2 @ 3104fps) at 700yds Sunday and the group drifted about 12 inches with slight to no (2-3mph) wind.
Really, either will do what you need.