The non s models always have a different design. For example 3GS to 4 was different design, 4S to 5 was different, 5S to 6 was different. However nothing software wise was ever different on the regular number model from the previous year's S model.
However the S models always add a feature only they have. 4S had Siri, 5S has slow mo and Touch ID, and the 6S is rumored to have Force Touch.
So based on that I usually find that waiting for S models if you can is. better buy.
Well I guess I just remembered that you can't use Apple Pay on the 5S but still I find the S models add extra features that are way better than the redesign.