This always seems to be my dilemma as well, if weight isn't an issue I go with rails. The last couple I bought were from mountain tactical for Tikkas and I think they are great for the money. The ability to perfectly position the scope and also being able to mount an anti cant level to the rail are why I go with rails.
Agree with Sockeye66. You have some additional flexibility with rails. If you know the scope and have a fair idea of how you want it mounted front-to-back, direct mounts might work and save some weight. But if you had that info, you wouldn’t have asked.
Looks like everyone is covering the pros and cons really well here, but let us know if you need help with either version. In general we find that a pic rail adds about 3 ounces to the build, though that is dependent on the rail's weight.
I haven't had any issues, the rifles I have them on that actually bridge the action opening would be a Savage 111, Savage 12, and a Browning A-bolt. The Tikka's are a non issue as the ejection port is to the side.