On paper, with current values, AST + SGE seems better for both progression and damage.
- Chain Stratagem is noticeably weaker at the start of expansions, since crit buffs have more impact much later in gear progression.
- Lilybell doesn't actually seem that good, since the WHM needs to be the one hit in order to trigger it. (though maybe there will be an abundance of J-Wave Style Damage output)
- SGE's HPS is significantly higher than SCHs ~and~ SGE has no opportunity cost for using Addersgall Healing oGCDs.
- Macrocosmos

SCH with Expedient may also be an incredibly powerful prog and uptime tool, but I do not personally believe that ability alone will tip the balance in SCHs favor.