Playing as Asch

Playing as Asch

Are there any Benefits from Playing as Asch that I should know about?
Like:

- will Luke get anything out of this such as AD Skills, etc.?

- If I give Asch a C. Core, will that help Luke in any way?

- Are there some AD Skills/Artes/Equipment etc. Only Asch can get that I should take advantage of?

And

- Once I switch back to Luke, Will I loose anything to Asch such as certain things being inaccessible because Asch holds them(ex: C. Cores, Equipment, Fon Slot Chambers, etc.)

You know, stuff like that.
Because I don't want to loose anything important from playing as Asch.

Or to put it in simpler terms:

Is there anything I permanently GAIN and/or LOOSE from temporarily playing as Asch and then switching back to Luke later on?

Please Explain if you can. Thanks!