I had (wish I still did) a Remington Stainless Sendero in 300 RUM...it had a stainless fluted barrel and I promise would shoot 1/2 inch groups at 200 yards with Factory ammo...Not everyone likes the H&S precision stock, but I do (it is not a McMillan though). This rifle again would be my first choice...but in the Browning I love my Stainless Stalker and it is my go-to rifle...it is chambered in 30-06.
I love the Police model too with the heavy barrel...since I already have the LTR, I would likely go for the full size model that you mentioned to have a pair of similar rifles just for the fun of it.
I like them both (Browning and Remington) I do like the factory trigger on the Browning better though...and the bolt throw...decisions...this is part of the fun.