Butcher told BBC Sport: "Rio seems to have become far more consistent. He doesn't miss a lot of games. He is very strong and solid and has developed into a very impressive central defender.
"He has got pace, good ability on the ball, so on balance I would give it to Rio, but it is a very close call and John Terry is someone I would be very happy to be given the England captaincy."
He added: "Rio was out there in Trinidad. He didn't have to be but he wanted to be. He has taken on board the extra responsibilities, doesn't make anywhere near as many mistakes as he has in the past and his concentration and sharpness is excellent.
"John Terry has had injury problems and he is the sort of bulldog figure who has great captaincy qualities. I love John and the way he is prepared to put his body on the line and himself on the line.
"I love him as a player and see something of myself and the way I played during my career. He comes back from injuries quickly and is desperate to play. I think he is a great leader and a remarkable person.
"Rio is someone England miss when he doesn't play and Manchester United miss him when he doesn't play. He has been successful as captain at Old Trafford and he has been following a long line of great players.
"Sir Alex Ferguson doesn't hand that honour out lightly or frivolously, so it is a sign of Rio quality and personality that he gave it to him.
"Rio has settled himself down, matured and is now a phenomenal player."