Are the Mercury and Galaxy sister ships?
Yes. There are a few differences in layout, espeically in the area of the cinema, and in assignment of spaces, but they are pretty minor.
Celebrity's web site wrongly refers to these two vessels as part of the Century class. In fact, they are a different design from MV Century and thus correctly called the Galaxy class. MV Century is a "one of a kind."
And how do they compare with the Summit/Millennium ships that we have previously sailed on?
The ships of the Millennium class (GTS Millennium, GTS Infinity, GTS Constellation, and GTS Summit) basically gained a specialty restaurant and lost a night club compared to MV Galaxy and MV Mercury. Of course, some facilities like the cinema moved to different locations in the newer class of vessels and there are some differneces in layout. Overall, these ships are pretty comparable. The newer class is only about 10% larger than the older class, so the difference in size is not really significant.
Are their staterooms similar (Concierge Class)?
They are pretty comparable for similar categories. There may be minor differences in layout and furnishings.
Have a great cruise!