The Monkees didn't write their hits (Boyce and Hart wrote a lot of stuff, as did other pro songwriters at that time) or were trusted to play much of anything on the records (except singing) until later in their "post TV" career that generally sucked. Nesmith was a good writer and musician anyway.
The Beatles had more creativity crammed into a relatively short time than anybody before or since, and the Stones were and are a great R&B band with undeniable charisma and style and great rock and roll...I saw the original band with Jones in 1966 and they killed. Still do.