Can't compare. Really depends on job scope. No difference between ministry and SB if you're in a supportive role (HR, OD, Finance, etc). Ministry has inflated titles however so AD in SB is equivalent to at least SAD in ministry.

Do also note that any slightly interesting job in a ministry will most likely be filled by a scholar. If you're not scholar, I highly recommend you don't join policy in a ministry (even if you can) where it's a scholar's playground and you'll end up seeing your scholar peers rise up like crazy.