You will see a performance increase. I think the 9500GT competes with the old Radeon HD 4650. The Radeon HD 6670 is a pretty decent mainstream card and it would be around as powerful as the nVidia 9800GT.
Will it last you 3 - 5 years? I suppose so if you play games at lower resolution and lower graphic settings in the future. If you cannot afford a HD 7750 (equivalent to about a HD 6770), then the HD 6670 is probably your best option.