I've a Tikka T3x CTRin 6.5cm, and i've owned a Reington 700 LTR in 308. Without any modifications, the Tikka actions are much smoother than stock Remington 700s. Tikkas also have way more features than the old school Police and LTR such as oversized boltknob, side bolt release, threaded muzzle, and detachable magazine. Regarding accuracy, the Tikkas shoot very well and are generally considered the most accurate production rifles. However, the Remington 700 Police and LTR models have a great reputation for accuracy as i think Remington Defense builds these models separate from the regular line of 700s, at least that's what a Remington Defense rep said on thsi forum a year or so ago. For sure the pre-RR prefix Remingtons were great shooters, but in general i think you can't go wrong with a Police or LTR model. It all depends on how many features you want.
The Tikka CTR and R700 Police/LTR are all about the same cost, so i think you get more for your money with the Tikka CTR.