You can show up to the same place and get the job done with either one.Then it becomes shades of grey,and preferences.You can go elk hunting with either,and you have to place your shot with both.
Study your load manuals.My Nosler compares 7-08,280,and 7mm mag,all with 26 in bbls.In a way,that is useful for comparison,but then,who carries a 26 in bbl 7-08?And what happens to a 7 mag if you shorten the bbl to 22 in?
I think for mostly deer at reasonable hunting ranges,the 7-08 is a great choice,particularly with the 139 to 150 gr loads(and,the non-lead bullers,a touch lighter).IMO,as you start stuffing the 160 gr + bullets to fit in a 2.800 mag box,you get to diminishing returns with the 7-08.Still,with a 22 in bbl you would likely get 2600 to 2650 easily.Bullets are designed to expand and perform within velocity ranges,often above 2000 or so.The 7-08 will give the 2000 fps at 300 yds,no problem with a 160 gr bullet.
A typical .280 might have a 24 in bbl and can longer seat 160 to 175 gr bullets.Velocities will be up near 150 fps faster,which translates to nearly 100 yds farther range to still deliver the 2000 fps .
What is interesting is how near to 7mm Rem Mag the .280 comes,generally within 70 or 80 fps.
Now,in the Nosler book,there will seem to be one powder that exceeds the rest,like Re-19 in the 7-08.QWhile I do not discount Re-19 in the 7-08,lets not forget that 26 in bbl.I looked at the cluster of second fastest powders.I set aside the H-870 load in the 7mmRem,too.
Study the numbers,they tell you some.,But,then look at the whole package,and what you are trying to do.If I'm carrying a 7 1/2 lb rifle with a 24 in bbl and I likely will hunt elk,I'd go .280,and shoot 160 gr + bullets.
I could still do all that with a 7-08,just a little less velocity.But if I want a 6 lb,22 in bbl handy little woods gun,the 7-08 is obvious.
Myself,I would lean to the 280 over the 7 Rem Mag more likely,but,once again,its pure preference and shades of grey.