.270
may be one of the better all 'round deer cartridges (it and about 30 others
) Will certainly do the job - it shines with bullets in the 130 grain-class.
Do you reload? If so, there's bullets in the 90-110 grain weights that will make dandy varmit loadings.
The "varmits & deer" question boils down to what will you do most of - & maybe, what size deer will you attempt to take.
For an "all-round" catridge for "varmits & deer," I'm thinkin' more along the lines of a .243 - especially if you want to do more varmits than deer.
No question, I'm a .243 snob, but I've got a .270, 7-08, .308, .30-06 (+ some larger & some smaller). Each are perfect, each fill "that niche" that the others don't quite cover - either due to rifle weight, action length, recoil, trajectory for any given task/bullet weight/target. & to be perfectly honest, I could just as easiely "get by" with perfectly suitable cartridges that I don't have (= .260, .280s, etc.)
My take, if you'll use it more for deer, get the .270 If more for varmits, get a .243 Be happy with your choice, shoot a lot & get good & never look back. Please do pick a bullet/loading suitable for what you intend to shoot.