If you like your '06, have it rebarreled and never look back.
Otherwise, choose something you like and go for it. 300yd Whitetail is doable with just about any centerfire rifle.
Do you reload? Do you hunt other big game besides deer? (black bear etc.)
For 300yds and in, the '06 is pretty tough to beat, but the 270Win is just as good, if not better for that role.
If some is good and more is better, then too much is just right.
My mind is a raging torrent, flooded with rivulets of thought, cascading into a waterfall of creative alternatives