Ok, the OP ask about .25-06 and 270. I have had a few of each and still have a 270. Here is what I will say about these two rounds, IF you reload, that opens a lot more doors. IF you do not, factory bullet selection on the 25-06 is somewhat limited. The same can be said with the 270 in lighter weight bullets. The 270 has more options in 130 and up weight bullets but that will go against your recoil requirement.
Either will kill deer at the range you are asking about with no problem if you put a bullet in the proper location.
If someone were to tell me "I will buy you a new rifle (between these two cal.) I would go with the 270. Reasons 1) wider range of good bullets 2) I am like an earlier post, I have way more time behind a 270 than a 25-06 (guess you could say comfort level) 3) (assuming you don't reload) around here 270 ammo is everywhere and not so much with 25-06.
Now there are ways around recoil, 1) add weight to the gun 2) put a good recoil pad on 3) reduce the vel of the round 4) reduce the bullet weight 5) muzzle brake (a lot of people don't like them, but they can really help) 6) have the stock fitted to the shooter (it can make a big difference)

If you are open to other cal. I would look at 6-06 (based on your two other parent cases) or a 6.5-06 (once again based on your parent cases) but only if you reload. If you don't reload but are open to look at other cal, there are several 6 mm round that will do a fine job on deer at the ranges your looking for. There are several good bullets with high BC and also light weight bullets to plink/varmint hunt with. Same can be said about 6.5 but the bigger you go in cal. you start cutting away at lighter weight bullet options.

Last edited by pullit; 07/09/20.

I may not be smart but I can lift heavy objects

I have a shotgun so I have no need for a 30-06.....