As to whether it's competitive or not, that's a personal opinion. There's a reason the Anschutz 64 and 54 took over the firing lines of the world.
I asked Leon Wigger about the older rifles, he having won a number of National Championships when Remington and Winchester rifles were common and many were still on the firing line, and he said his score was better when he started shooting Anschutz rifles. That is a pretty good recommendation.
Winchester and Remington did not improve their smallbore rifles, they did not keep up with improvements and the market walked away. This is not to say the M52's, or M37's, or M40X's, or even the H&R M12 are inaccurate, they are accurate, but the rifles with the old stock configurations and triggers are harder to shoot consistently. The Army mandated three pound triggers, which are fine on a Garand, but most shooters today are using triggers from an ounce to eight ounces. I have pulled a lot of three pound triggers and it is as jarring as slamming a hatch each pull.
I took pictures of the 2010 Irons National Champion at Camp Perry, Mr Charles Kemp. This is Mr Kemp and his M52 D rifle.
About the only thing that was a M52D was the action and the trigger, and that trigger was modified to an 8 ounce pull. However the Winchester action is an outstanding action and if all the bells and whistles are attached, the rifle is capable of winning the National Matches.
I took this stock box Remington M37, made 1941, and shot in a 3200. I did win the 100 yard any match with the thing.
This is my 400-32X.
The gun club president has an identical Rem 37, though with an Eric Johnson barrel, and he shot it F class style at the Club. With a bipod and a rest he did this at 100 yards during a small bore match
These older rifles will shoot if the barrel is good and if they are well bedded. I remember one Lady who had a Win 52 action in an Anschutz prone and she was shooting inside anything I was doing. Her action had a modified trigger. I am of the opinion, having seen enough Win 52's on the firing line, and seeing the groups, that the original rifles are inherently accurate, just that the old style stocks and heavy triggers make them harder to shoot consistently. It is a shame Winchester walked away from smallbore because the action is an excellent basis for a target rifle. The Remington M40 action is being copied today and is the basis for an excellent small bore prone rifle.
I have been shooting small bore prone competitively for a number of years now and I am of the opinion that while you need good equipment to win, in the final analysis it is judgement and ability that separates the champions from the pack. The very good shooters are psychic in their wind reading abilities. I accuse them all of Witchcraft because I have been there, next to them, same relay, and they are seeing things that I don't, and making wind changes while my shots are being blow out. It has to be magic. They also have lot tested ammunition for their rifles and that makes a big difference.
I do not look down on older rifles, because I have a number of them, and they will shoot well.