It's been a few years since I've been to
MNSSHP, but in general, while some of the elements between the two parties are fairly similar, to me the parties felt very different. Both were a lot of fun and I can't wait to go again (to both).
Parade: WDW's Boo-To-You parade is much more elaborate than DL's Cavalcade. Prior to the WDW parade, the Headless Horseman rides the parade route. It's really cool! I love the Haunted Mansion sequence in Boo-To-You (the dancers with the shovels are amazing). The DL cavalcade is cute, with lots of characters in costume. Last year (2015), they presented Paint the Night instead of the Halloween Calvalcade, but hopefully this year, the Calvalcade will return.
WDW
DLR
Fireworks: In this case, both shows are really good. DL's Halloween Screams has Zero flying (in place of Tinkerbell or Dumbo), but he's really neat. Jack Skellington is the host, so if you're a Nightmare fan, that should be a treat. I don't think anyone flies during WDW's HalloWishes, but they make really cool use of the castle and "surround fireworks". Some of the music is the same between the two shows.
WDW
DLR
Trick-or-Treating: WDW has treat stations with one big treat trail. DL has almost entirely treat trails (multiple treat stations along the path). In both cases, the trick-or-treating is pretty popular first thing at the party and tends to be more manageable by the second half. The treats themselves seemed pretty similar.
DLR (WDW was pretty similar):
Character Meet and Greets: Both parties have a lot of character meet and greets. You'll find some "rare" characters out (e.g., the seven dwarfs at MK, several villains at DL).
Dance Parties: WDW and DLR both have/had character dance parties, which can be fun if you like to do that. I think they're nearly in the same place (Tomorrowland). They're cute and pretty high energy, with some characters making an occasional appearance.
Castle Forecourt Show (MK Only): WDW has the new Hocus Pocus themed Castle Forecourt show. I haven't seen it for myself, but it sounds pretty impressive. DLR doesn't have anything quite like this, although there is a mini-show every time the Villians change out of the meet & greet location.
Pre-Party Party (DL Only, I think): Prior to the start of the MHP, DL usually has a pre-party in Toontown. You need to have your wristband to attend, but it's a good chance to do some early trick-or-treating and see characters in their Halloween costumes (usually these outfits are different from the ones you'll see during MHP).
Rides: At both parks, most of the big rides are open during the party. DLR has Haunted Mansion Holiday and Space Mountain Ghost Galaxy. None of the rides at WDW have a Halloween overlay.
Food: In both parks not all of the food venues remain open during the party. If you want to eat, I'd grab dinner before the party starts! Be sure to check out any special Halloween-themed items.
Merchandise: Both parties feature event specific merchandise (usually t-shirts and pins). At MK, the event merchandise is limited to party-goers, but DL (usually) sells the merchandise all day.