Some 48 Volt controller will work with a 60 Volt battery pack while others will not so it depends on the particular controller whether it will be okay with a 60 Volt battery pack and motor. You could take a chance with the 48 Volt controller and see how it does, or install a 60 Volt controller along with the new battery pack and motor for a less chancy installation.
Please let us know if you have any questions.
Presuming that both the 48 Volt and 60 Volt motors are being powered by controllers with the same Watts output then the motor's Watts rating affects how much power it will produce and its Voltage rating has no effect on its power.
A 60 Volt motor would run at reduced power and speed with a 48 Volt controller and battery pack.