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). This comparison is based on the parties in 2016. Everything is subject to change!
Parade: DLR introduced a new parade last year (Frightfully Fun Parade), which is much closer to a full parade than the previous Cavalcade. Now both
MNSSHP and MHP feature the Headless Horseman riding down the parade route ahead of the parade. The Frightfully Fun Parade has some elements that are similar to Boo-To-You (I love the Haunted Mansion sequence in both parades with the dancers with the shovels that are amazing), but generally it is its own parade. Both are very good, but Frightfully Fun is a bit darker overall. Boo-To-You is one of my favorite parades at MK.
Headless Horseman (MNSSHP, but same look at DL)
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, although, if the weather is very hot/humid in FL there might not be as much chocolate-based treats.
DLR (WDW was pretty similar):
Cadaver Dans: Both MNSSHP and MHP have the Cadaver Dans, but I personally think the MHP version is better. MNSSHP's group walks down the parade route and are dressed to fit into Frontierland (I'm not sure is they perform at other times or places during the party). MHP's group are dressed as the undertakers for the Haunted Mansion and perform from a raft on the Rivers of America at set show times.
DLR
Dance Parties: WDW and DLR both have character dance parties, which can be fun if you like to do that. I think they're nearly in the same places: Tomorrowland and Frontierland.
Castle Forecourt Show: WDW has a Hocus Pocus themed show on the castle forecourt stage. It's very high energy and features a number of the villains characters. MHP doesn't have anything quite like the Castle Forecourt Show.
WDW
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 MNSSHP, Villains at MHP). At DLR a rotating set of villains greet the guests in Town Square (so they do have to cut the line so they can clear it before the parade starts).
DL
Rides: At both parks, most of the big rides are open during the party (some attractions are closed, primarily because they're being used for treat-trails/stations). 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. MNSSHP seems to have more items that are billed as party-exclusives.
Pre-Party: Upon entering MNSSHP, guests are invited to head down a pre-party treat-trail to get some candy (and your trick-or-treat bag). DLR has (for the last few years) had a pre-party in Toontown. The pre-party featured trick-or-treating and character meet and greets. It's a lot of fun and a great way to start the party with a lot of candy!
Annual Passholder: If you're an annual passholder, then MHP also (for the last few years) has a special treat location for AP holders. It usually includes some kind of exclusive treat or item (e.g., one year it a draw string bag, another year there was a rice-crispie treat). I don't recall any AP exclusive location/items at MNSSHP.
Tickets: Both DLR and WDW pre-sell tickets to their parties on their respective websites and you can purchase them in person on site. That being said, DL's MHP almost always sells out in advance (see
this post for dates of last year's sell outs). MNSSHP tickets tend not to sell out as early (or at all). DLR generally announces the party dates in mid-summer (it's been early July for the last few years). WDW announces their dates in early-Spring (
dates for 2017 have already been announced).
It will be our first Halloween in Disneyland! So excited, and itching to start laying down some plans. The party leaves a big question mark. I look forward to the responses - even if it's just more guesses! 
