What should I do if a new cabinet is smaller than the old one?
Some generic pieces of advice here:


Buy cabinets with a bigger footprint.
If a smaller footprint it can work out if there is an equal distance around the bottom.  You can lay down mosaics to make a border.  It really depends and we would need to see a picture for more help.
Anytime you tile a bathroom, tile the whole thing.  Cabinets should sit on the tile.