You'll probably save memory. Even though the RAM is 32 bits wide, it can be accessed with a granularity of 1 byte, so you can store two uint16_t's in a single word.
The effect is most obvious if you create not just a single word, but an array. Create an array of 1024 x uint16_t and it'll use up 2k of RAM. If you use uint32_t, it'll require 4k.