Factory or not
There are a number of things to keep in mind, when deciding a choice, that are not so far mentioned.
The factory exchange offers; New, Rebuilt or Overhauled engines. The difference between "rebuilt" or "overhauled" is not clear. The best explanation, that i've heard, is this; rebuilt is an engine that has only those components that still meet the new engine spec. minimums so are retained. Note the caveat "minimum" not the same as you would expect of an actual new engine. The overhauled engine retains all components that meet approved minimums and should be good until the next scheduled TBO. The actual specs used are not published or easily found. With regard to the returned engine being reimbursed. The factory will only reimburse if the returned engine is good. A knackered crank or a suspec case will mean nothing is likely to be reimbursed. Could be a very expensive option then and has lead therefore to many operators choosing a local (UK) rebuild as the best option.
The benefit of a local rebuild undertaken by one of the companies already mentioned above is that you remain in control. The engineer can advise you of any components they consider is passable but could, even if not likely, let you down. Try getting the factory to honour any of its warranties after a couple of years have passed or the engine is only a few hundred hours into the TBO. The manufacturers expect you to have a top overhaul on half life. Lycoming and Teledyne cylinder problems are another reason for a local rebuild. This allows you to specify after market cylinders with much better life expectancy such as Superior.