Having flogged both bikes and bits in the past I’d say on balance your better to split. Most people shopping for a whole bike will be looking for a local-ish look see and pickup rather the than see what comes through the post (plus you probably won’t fancy boxing up and posting the whole bike), and they might be put off by having to find the couple of parts you’ve already transferred to another bike.
On top of that we’re heading into winter, so now is the time potential buyers minds turn to assembling a bike over the colder months, if you were flogging it in spring/early summer then you perhaps have a better chance of getting a sale form someone keen to just get rolling ASAP…
Splitting generally means you’ve got a better “Hit rate” i.e. there’s more people looking for a pair of forks or a crankset and these are smaller, relatively cheaper and easier items to post.
It’s just a bit more time consuming in terms of popping all the parts up on classifieds, ebay or wherever you choose to flog them, and packaging up to post, but taking a bike apart is often pretty quick and can be strangely therapeutic (IMO)…