We have both.
Some of the advantages of hard side (of course it depends on the piece)
- It's waterproof
- it can be lighter
- it's significantly easier to clean
- you can stack another bag on it
- it is sturdier
and soft side
- expands when you need more capacity
- collapses for storage
- usually has outside pockets
- Can have several compartments
- Doesn't usually show wear as easily
We also have a hybrid bag (or did, not sure if it's in the current rotation or if it died) that has a hard bottom and sides, but a soft top to allow for the benefits of both.