What are the advantages/disadvantages of press fit bottom brackets compared with threaded?
Advantages:


It's cheaper to manufacture cups, even with fine surface finish and reasonable tolerances than threaded shells.
Especially with carbon frames there was an issue with inserting threaded shells which needed to have perfectly parallel faces. With press-fit cups and cartridge bearings having some factory loose, the tolerances are not so strict.
A press-fit bearings are just a bit quicker to install. The difference may not be huge, but is significant when assemblig thousands of bikes.
Removing a threaded bottom bracket after a few years can be a daunting experience. Especially when no grease/thread glue was applied and it was mounted on a steel frame.
Thread could easily be damaged when replacing a bottom bracket without care.
A new standard is always a good opportunity to use for the advertising department.
Although sometimes recommended, no tools are usually needed for installation.


Disadvanteges:


Press-fit connections wear out more quickly when you replace the bearings often.
Bearings which have to account for imperfections in cup mounting, don't last quite as long.
It is possible to re-thread a damaged bottom bracket shell thread while it would be way more complicated to replace press-fit cups.
Bearing removal requires care and experience to protect cup surface from damaging.


There are more diferences, but they are more specific to a given type of bottom brackets, and the ones above are more general. Most of the advantages of press-fit are felt by the manufacturers rather than users, although I do appreciate the ease of installation of these bottom brackets.