My 2 cents ....first I am a huge fan of the 7mm (.284 dia. rounds). My thoughts have evolved or are evolving .....
My dad is of the age who beleive that all things start and stop with the 06, usable hunting weights of 150-220 grains can be used on anything in NA...true enough. I happen to think a 160 gr 7mm will do what is needed and 175's can be used but are not ideal if big bears are involved.
I got my dad a Ruger #1 in 7mm rem mag a few years ago for an antelope hunt. He used 160 gr partitions and did just fine, even used up his ammo on the prarie dogs after his goat was down. That was fun and what a mess! But I admit his 06 would have worked just as well with 165's because it did on previous goat hunts for him. Why change? I persuaded him while it worked it was not needed.
In elk camp this year conversation around the table was normal and we all dicussed what we were using. No real surprises, a 270 WSM with 140 AB, 7x57 with 140 AB, a 280 rem with 160 part, a 2980 AI with 160 part, a 257 wby with 120 part (deer hunter) and a 338 win I dont recall the load. When silence came to the conversation the guide at the table, a well educated fellow with 6+ hunts a year to his credit, tried to escape the conversation and tent until I pressured him for an opinion. Probably very unfair of me, but we were all long time sports in that camp. This young fellow (late 30s?) uses a pre 64 Win in 30-06 with iron sights (williams peep) and 180 gr partitions to back up his hunters. He knows is rifles and loads! This was a working rifle, not fancy - wood stocked and scarred up .... He says it can be needed and the 180gr partitions do the job. He proved that this year, as a sport needed help anchoring his first elk.
Later during idle times in the hunt we had the chance to talk about rifles, he uses a 300 win with 200 gr partitions when he hunts for himself. As a side note he also has is family members use the 06, for elk and other game, if I recall they were in the young teen years and he was proud as he should be that his daughter was a crack shot with it! I beleive that at that point the conversation was framed around chasing elk that were hit but not put down.
I think the discussion about caliber is incomplete without bullet identification & selection. The Partitions have a legacy reputation of performing well, very well. As the guides of this camp agreed that exit holes matter, two points to bleed from and the more bleeding the better. We also talked about bullets that come apart on bone and dont give an exit hole, this is a lot more prevalent than the marketing teams would have us know.
The 06 vs 270/7mm will rage on, like everyone has said take what you shoot best. Most guides will add that you should practice a lot with a chosen load. Stick to that load and bring plenty of ammo on your hunt. I have seen guys drop 7K on a hunt and only bring 6 rounds for "extra special" handloads as well as guys try to decide if they should use Remington, Winchester or Hornady ammo for todays hunt. The stories go on and on...
I think I would go with the 06 and 180 gr Partitions for under 350yds, all things being equal.
A free opinion and story ....we all know what thats worth !