I was late to the 6.5 world. Happily used a 280 Remington for years, then had it rebored to .338 using the 280 chamber. It was a great SE Alaska deer cartridge.
My first 6.5 was a well-used 6.5x55 96 Swede, followed by a Rem 700, a couple of Ruger 77’s, the last one was a Sako 75 stainless which got sent to my grandson in Alaska, who had been deer hunting with an AR15 in .223. He’s happy with the 6.5x55 and is able to find some decent factory loads for it as he doesn’t handload, yet.
I bought a 6.5 Creedmoor to replace the Sako sent to the grandson. Now that I don’t hunt anymore I can still enjoy shooting the 6.5 CM at the range. Little recoil, great accuracy, and just lots of enjoyment. I wouldn't hesitate to use it on a deer, given the chance.
Also tried the .260 Rem when it first came out in the Model 7 and the one I bought was a dog for accuracy. Later got one in a Sako 75 and it was a good shooter.
Never had a 6.5-06, though not from lack of interest. It would have been a better all-around cartridge than the 25-06, which was another favorite of mine for several years.
A note about that Remington 700 6.5x55. I purchased it used from the LGS and never could get it to shoot accurately. Traded it back in on something else. Was in the shop later and chatting with one of the local gun guys that I knew pretty well. We watched a fellow checking out the rifle and I mentioned that I had owned that rifle and never could get it to shoot well. He smiled at me and said “Yeah, neither could I.”