I don't think it makes any difference, but 'bubbles' sounds more kid-friendly.
Six of one, a half-dozen of the other.
I suppose there's a technical difference, in that suds are smaller and frothy, where bubbles could be larger and less frothy, but from a 3-year old's perspective, they're equally as fun.
All suds are bubbles, but not all bubbles are suds.
Student or Learner