Everybody will have a slightly different opinion. If you plan to alter it or get into long range shooting look at the rem. The actions are good and there is a huge availability of aftermarket parts and gunsmiths that work on them. I have a couple and they do well.
I also have 2 Tika T-3's. Love the light weight and smooth actions. Both shoot well. My 300 WSM
will shoot a 3 shot group of 1 1/2 inches at 300 yards. Triggers are one of the best for a out of the box production rifle. You are limited by the lenght of the magazine. You can't run most bullets out to touch the lands and use it as a repeater. The cartridges made up that way are too long to fit into the clip. That's my biggest beef with them.
A 30-06 will take care of you for the shooting that you are doing now. You might consider a different caliber as you look to the future. If you see any long range shooting in the future you might think about something that shoots flatter and faster. Perhaps a 7mm or one of the fast .30's. If its only for deer look at one of the .26 caliber's. They will have less recoil than the 30-06 and will do as good of a job. With the new bullets in the 27 calibre it should also be considered. Good luck in your search. Bruce