Headphones Bluetooth vs Cable

Hi folks , was wondering if there is a difference in sound quality? , have an old sony xb 50 in ear set that i use when i run, i find the sound quality to be awesome, my wife has a cheap blue tooth set, i dont enjoy the sound quality at all, (she says its awesome) ,but it is so convienient especially with running , no wires and easy to control. Is there an affordable compromise? or do i have to drag wires everywhere?.