From what I understand, tin-based sources are easier to work with because they are point-like. All the energy is produced from a tiny droplet. Synchrotron sources produce much wider beams, that need to be re-focused properly.
Synchrotron FELs are already used, and their construction paid for due to their scientific uses. Building new ones would require new synchrotrons, which are more expensive than the crazy "hit molten tin drops with lasers to make a plasma" scheme the ASML machines use.