While some of Carmen's futility against Fullmer can fairly be attributed to age and wear, all you gotta do is watch those fights and see how huge Fullmer looked compared to Basilio. Old or no, that was gonna tell in a fight between those two. Same boat here. Basilio has nothing to keep Lamotta off him, and he can't box his way out of it.
Basilio is the more skilled fighter, but Jake is the bigger and stronger man. Carmen will give a hell of a fight, but LaMotta will keep boring in. Basilio will tire out late enroute to a TKO loss.
LaMotta was pressed by ex-welter Cerdan when they fought for the title and Basilio is arguably better. One of the areas where he is better is in weaving punches - I could definitely see a situation where Basilio does the better punching and that costs LaMotta rounds inspite of his relentlessness and aggression. Can LaMotta make Basilio welt? I don't think he can...over a distance like ten rounds I think Basilio is a fine pick, but no money going down over any distance, because I feel it's a case of what the judges will like.
Not necessarily a better middle though and to be honest LaMotta just man-handled and beat up Cerdan who was courageous but never truly threatened LaMotta with anything he did. LaMotta might be a better match-up for Basilio than Fullmer though as Basilio wouldn't have to go looking for him, unlike against Fullmer who had his bicycle on a lot of the time, but in a sense it's also worse for him as he would be fighting on the inside against a bigger, stronger man who was even more adept at that type of a fight than Fullmer, who always had the better of Basilio in the exchanges. Basilio's sheer toughness and will keeps him in the fight, but he would get the worst of it for the most part. On his night Basilio could outpoint LaMotta who did not always turn up in best form in a "herculean" effort, but at their bests LaMotta would take it. He's the bigger and stronger man in a favourable match-up for him. LaMotta's real problems were against fighters who could take advantage of his slow feet, not those who tried to match him in strength. If anyone wants to make a case for Basilio though they should bring up the Villemain fights, but I'm not so sure of LaMotta's conditioning for those fights, or pretty much any fight he had after the Billy Fox fix aside from his title-winning effort against Cerdan. He was in his prime during the mid 1940's, in my opinion.
