West Knoxville was the fast growing part of town when I was growing up there in 70s and 80s. Problem is that "West Knoxville" has grown all the way out to the Loudon County line.
South Knoxville into Alcoa/Maryville has really taken off with the completion of the Pellissippi Parkway extension. Much easier to get around and real estate has appreciated.
Job location and school system (if kids are a factor) have always been my biggest consideration when relocating to a new town (I've done it 9 times now).