I've used em both quite a bit, and have gravitated to the 6/06. Now part of that could be that I work with the big 7's quite a bit and now that I run a 6/06 and a 7 I just don't see a need and or a want for a 257 Wby.
The 257 will send 120's down range @ 3300 (on top end) and I can do that and then some with my 7. And my 23" .270's will send 130's down @ 3150 so I don't see much value to the 257.
With my 6/06 I've had two tubes (but have worked with 5 others) and I've found that they'll send the 85 TSX down the tube @ 3500 to 3600 lot of powder depending. This is with a 25" tube on my 6/06, and my work with the 257 Wby has shown me that 3500 is pretty darn standard with the 100's and I can get it to 3600 but that's about the end of the game.
Tween the two I've been able to discern no diff in killing power and ability from big to small in regards to big game.
Now I am a believer of fast and slow tubes and I've no doubt that a fast 257 tube will go over 3600 with a 100 but not by much. Same with the 6/06, my first tube would run a 95 NBT @ 3500 with R25 and R22.
But IMO those kinds of speeds are not the normal, more like abby normal...
Guess I'd look for an action and if you found a standard bolt face I'd build a 6/06 and if I found a magnum action I'd build a big 7 of some sort...grin
Lastly, when I built my 6/06 I really had long range yote run in my mind and it's done very well at that for me. And it's taken deer out to 634 yds with no issues as well as an ark or three of deer/lopes and various other critters.
I also sorted out that the lil 55 NBT @ 4K+ worked very well on called in yotes during the prime pelt time. Incredibly pelt friendly, now the 70 NBT is another thing. The 70 is what gave my rifle the name "El Gato". When my buddy shot his first yote with the 70 NBT in the spine he remarked, man you could pull a cat thru that hole....
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Best of luck to you, either choice will do you very well.
Guess I'd also consider what else you have for bigger guns in the stable. If you have .270's, 7's and such then I'd go 6/06 for sure.
Dober
