Actually, we haven't a clue what velocity the DF-21 hits at. Whilst it's been declared to be at 'operational capability', at no point yet has there been any announced or observed tests - the hopes of watching a test fire was why there was quite a significant interest in the recent(ish) fleet exercises.
I haven't actually seen a definitive statement as to the warhead, either.
That said, comparing to other MRBMs is a good rule of thumb. It is following a ballistic missile flight profile, so it's going to be falling pretty close to vertical during it's terminal attack. I'd say a free-fall penetrator is a pretty good damage model. The key is actually hitting with the thing - with a flight time somewhere the wrong side of a quarter of an hour, against an evading target capable of making significant speed (supposedly 30+kts flank speed for a US supercarrier)*.
Regardless, as noted, it's not really bombs or shells that are the biggest threat (until you get up to really big bombs, anyway) - the real giant-slayer of proper capital ships, from the Bismark to the Belgrano, has always been torpedos. Which, since they are usually delivered by either aircraft or submarines, both of which are opponents a battleship struggles to fight effectively, makes them doubly scary.
Underwater explosions are nasty - water's largely incompressible nature makes for some seriously unpleasant effects, and means that even a lateral, non-contact detonation can cause serious damage to a ship's innards, whilst the ideal hit - a heavyweight** torpedo, detonating a few metres under the keel amidships - is quite literally back-breaking.
* Of course, if the carrier is making flank speed and zig-zagging, it's going to be maintaining limited air operations at best. Which is, I guess, sort of the point.
** 650 lbs for a Mk 48, so big but not that big compared to some bombs that have been used for attacking warships.