It's more cost and power efficient to use 128-bit wide buses in combination with GDDR5 memory than 256-bit with GDDR3, so that's why manufacturers made the shift. It gives comparable memory bandwidth stock and higher bandwidth if the memory is OCed, so it's more flexible as well.
The two factors that you take into account when measuring memory bandwidth are the effective memory frequency (eg. 4000MHz) and the bus width (eg. 128-bit).
To answer your question directly: your old card probably used slow GDDR3 memory with a 256-bit bus width, so memory bandwidth should actually be higher on something like a GTS 450.