.30-06 vs 7mm Rem Mag Recoil?

I've got a Tikka M695 Whitetail Hunter in .30-06. I've cheated on the recoil, and have had a recoil can and a Limbsaver pad installed. I've used it as my go-to deer rifle for years, and kinda know what to expect.

I traded a while back into a Steyr Pro Hunter in 7mm Rem Mag. It's just sat all winter long, and I've not shot it or even scoped it. Well, I've arranged for a scope (a Zeiss Rapid-Z 600) for it, so it's about time to scope it and sight it in soon.

Question I have is: recoil-wise, how do the two compare? I've read on "recoil charts" that they're fairly comparable. I'd assume that it depends on how the stock of the rifle is engineered. I know the Tikka has a well earned reputation for thumping your shoulder, and mine used to before I did all that work on it. I've read that the Steyr is a good shooter and the synthetic stock absorbs more recoil than (for example) a Browning X bolt or a Remington Model 700 in the same caliber, but how about vs. a .30-06?

What's y'alls experience?