For TLS much larger keys are typically used, "The recommended minimum key length is 1024 bits, with 2048 bits preferred, but this is up to a thousand times more computationally intensive than symmetric keys of equivalent strength (e.g. a 2048-bit asymmetric key is approximately equivalent to a 112-bit symmetric key) and makes asymmetric encryption too slow for many purposes."

Source: https://www.internetsociety.org/deploy360/tls/basics/