Think Hubble could do the same since it so close. My basic understanding is James Webb is better suited for ultra deep space observations, because it doesn't care about dust as much.
No, the reason JWST is better for ultra deep space is because the expansion of the universe redshifts the peak of the light emitted by the really old stars into the IR band. Also it has a bigger mirror so it can see fainter stuff, which things further away tend to be.