You can use any slot for Divine Smite

PHB errata:

Divine Smite (p. 85). You can expend any spell slot, not just a paladin spell slot.

Eldritch Smite is unclear

On the one hand (after needing a tweet from one of the creators and an errata to clear up Divine Smite) you would hope they did pay more attention to this, and the different wording is intentional.

On the other hand why would it work differently?

I think this is another case of oversight, waiting to be erratad.