Words in "всё еще" have meaning "still".
Words in "всё так же" have meaning "as before/in previous case".
P.S.
Second phrase can be used as: "В первой комнате чисто. Во второй всё так же." = "First room is clean. Second is the same." (second room is the same as the room before)
P.P.S.
Em... Maybe this is bad example. "всё так же" literally means "all things are the same (as before)". But when we use "всё так же" we mean not "all things", but mean "things from the previous case or previous time". "State of cleaningness (!) in the second room is the same as in the room we mentioned before). Wow.