"As did I" vs "So did I"

Which is the (more) correct response?

Me - "We have more tweaks for the ABC job"

Other - "Really? I thought we'd completed that job!"

Me - "As did I / So did I"

Thank you for any suggestions you can offer.


Both As did I and So did I are grammatically correct. As did I is very formal and may sound awkward in informal conversations. Another more informal way of saying it would be simply Me too.