Is my phone battery better / more capacitative than my laptop battery?
Until recently, all lithium laptop batteries were made up of cylindrical lithium-ion cells.  Now, many designs are using a lithium polymer (pouch) type battery in laptops.  This is allowing the thinner laptop designs.

The properties of the cylindrical and the polymer cells are almost the same.  The advantage of the soft pouch construction allows the same capacity battery fit into a smaller space, due to not having air voids between the cylindrical cells.

It is also important to note that many after market phone battery capacities are pulled from a data sheet that was printed in a Fantasy Land where everyone rides unicorns.