Lipo doesn't necessarily make anything faster. It's the power delivery/capacity per ci that makes them so desirable.
A 7 cell NiMH pack fully charged will be a higher voltage than a 2S pack fully charged. A 6 cell NiMH will be a higher voltage more than likely fresh off a charger. The difference between NiMH and Lipo is that NiMH starts losing volts almost immediately and they cannot deliver near the amount of current a lipo can.
With brushless (and probably brushed), volts is what gives you your RPM. Current is what gives you your torque. Lipo keep their current output from start to finish whereas NiMH lose current output as they drain. So, all things being equal, a same capacity and same V NiMH vs Lipo running side by side, you will see the vehicle NiMH will progressively get slower and lose it's punch. But the Lipo rig will retain it's speed (most of it, volts do drop, but not nearly as much) and it's punch right up until it's depleted.
Also, as for the capacity per cubic inch, Lipo holds a lot more power compared to NiMH cells of the same weight (higher power density), so you run a smaller pack that is lighter with the same or more capacity (more run time). This makes it so you benefit twice, less weight and more run time. Less weight in itself means more run time because your motor isn't working as hard.