Moyes has no doubt Chelsea defender Cole is a worthy number one but has been hugely impressed by the progress of Toffees star Baines this season. The 26-year-old, signed from Wigan four years ago, has taken his game to another level since narrowly missing out on a place in England's World Cup squad last summer.
Moyes said: "I have said many times I think Ashley Cole is the best left back in England but I think Leighton Baines is just a tad behind him. He needs to keep pushing very hard and improving, he needs to keep continuing his work and get better.
"You can see that Ashley Cole over the years has kept going but I think Leighton Baines has been the 'big mover'. He has done really well. I think he is getting closer to Ashley but in my personal opinion I think Ashley Cole is probably still England's best left back.''
Recent statistics revealed that only Manchester United playmaker Nani has provided more goal assists in the Premier League this season. Baines has also scored six goals himself this term, including penalties in the last two home games against Aston Villa and Blackburn.
It is a far cry from when he first arrived at Goodison Park when, despite his promise, Moyes regarded him as a raw talent. Moyes said: "For a while he wasn't sure if he was maybe out of his depth but I think he has grown into it.
"A lot of people have come here and not started in the team - for Phil Jagielka and Leighton Baines it has taken them to get into it in the way we want. But in a way I think that is right because it meant the players in the team were fighting hard to keep in it while we had people like Jags and Bainesy trying to push them.
"Leighton has matured, his football has got better. He has become a bigger part of the team now and is well integrated. We like him and think he has had a really strong season.''