I had the same choice some years ago and chose the 25-06 (Rem 700 BDL). But practicaly, theres not alot of practical difference between the 2 cartridges. The 25-06 is probably a better choice for varmits, and the 270 allows 150 grainers which are better for elk and bear if you ever want to hunt those. Both make the same noise so that probably isn't a deciding factor.
My 25-06 is super accurate with 87 gr. hollow points, and I've shot a bunch of hogs out to about 250 yds. Head shots at 125 yds. or less usually totally remove the head. Nice
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My sporter weight barrel, 4 x 12 scope, and hunting trigger make longer shots difficult. I now use 120 gr. partitions for deer after a few cup and core bullets blew up at close range on deer. Interestingly, a buddy has had some failures with 130 grainers in his 270.
I think whichever route you take, you won't go wrong.
Good luck!
Jim