Yes, it does have the same memory bandwidth. We're only talking about 24 pins here1. Only 64 of the pins of the SODIMM or DIMM are actual data lines, the others being used for clock/control signals, address lines, and to supply power to the chips. As SODIMMs have fewer chips, they require fewer address lines, and as they draw less power, they require fewer power and ground lines. Aside from the missing lines, SODIMMs behave in the same way as DIMMs. The overall bandwidth is the same.

1 - DDR SODIMMs actually have 16 more pins - 200 vs 184.