1ST PERSON DUNGEON DESIGN

Pretty much what Slash said, 1st person RPGs have a lot of unique puzzle factors, considering the perspective. What is obvious looking top down is not so obvious walking around. Especially timing based puzzles, since most first person RPGs tend to be moving in squares instead of gradually, you can't really 'hurry'.

For a modern take, you guys should check out Legend of Grimrock, which takes the old Eye of the Beholder style and updates it. The combat actually ends up quite action based, as often you are sidestepping around big beasts to avoid getting smacked. It also has many timing/teleportation puzzles, taking advantage of the fact that you 'throw' items linearly in front of you. One example is a puzzle where stepping on a tile creates a teleportation field to a sealed off area (but seen behind a grate), with a pressure plate on it. The problem being the teleportation field activates after a few seconds, and over a pit away from you, and only for a brief second. So the puzzle boils down to activating the field, counting the seconds, throwing an object just before it activates so it goes through and lands on the switch. You can get really complex with those sorts of mechanics, but you have to be careful to not make it a pixel hunt or completely obtuse.

I don't know if I agree its more work, especially if you have something that creates what the player sees based on a map or something similar. That is how a lot of the older games did it, you weren't designing it from the first person view, you were designing a map and assigning tiles/features/items to each square. Of course, it might be harder now because our current development tools, especially that this community use, are based around top down and not first person.

Damn, been meaning to write a whole lot but was too tired and then I forgot. Whoops.

First person dungeon crawler play out quite differently and can have a different kind of focus. There's more action-based combat like in Legend of Grimrock, but they often have the focus on long-term resource management and planning or setups, too. As you usually get very very few items on map and need to return eventually.
Rine made some very good points about Legend of Grimrock, which is definitely worth checking out.

This means it can have a focus on the exploration itself, with the treasure to find, secrets, secret quests (like finding hints or items in some dead-ends. often also hidden passages on the sides of walls, and sometimes text or scenes popping up like in the dark spire, where you may interact with the popping up event in some way, or some special rooms where people gather, special merchants, all possible), and just the feeling of eventually progressing and getting to new grounds.
3rd person dungeon crawling usually is more randomized and has no focus on that and the part of aesthetics, as far as I could see.
For first person you can build up huge nets you need to map out by hand or automatically, different corners to explore and go back to .. stronger enemies blocking your way, etc etc.
Which makes it important to have asymetric dungeons as otherwise it will be very difficult to travers without counting each pathway. They can form bigger symetric parts, but you need to tell the small pathways apart, like a large hall with doors on each side. In the same vein, you can make floors intentionally confusing by having a uniform layout. So can teleporters and other effects, such as fog-like endings where you can continue on to the other side of the map.
I suggest you look up layouts of etrian odyssey and other dungeon crawlers for that purpose.

In that sense, imo, first person dungeon crawler have a much greater emphasis on team building, resource management and exploration. They are often fairly slowpaced and allow for moving at your own pace and building strategies. Which can make them quite relaxing even when they are difficult. (which is where Legend of Grimrock and some older games like the might and magic series are rather fast-paced)
They can also have a far greater immersion by being left alone or even lost in some unknown parts and rather than straight out inbuild puzzles can go for pop-up additions at specific points (paper sorcerer does that a lot).

Third person dungeon crawlers are more fastpaced, rely more on continuous and quick item and equipment management, proper battle setup and reaction (don't get surrounded, avoid enemies that are too strong, anticipate different enemy speeds).
They often also allow to traverse with little setup, or, if you manage to do that, building really strong equipment you need to stay safe with (don't wanna lose it, now).
They can be enhanced by special effects on floors, such as traps, fog, darkness, speed modifications etc. Some also offer a roster of different characters to work with, or swap out. Story and immersion parts are usually handled outside the dungeon.

The biggest difference that strikes me is how much harder it is to navigate in first person. If you have played Phantasy Star, check out the maps. They are way smaller than you'd think after playing the game. Navigating becomes a lot easier if the dungeon isn't as samey looking and you have proper landmarks though. It becomes even easier with in game maps.

As has already been mentioned, first person dungeons also seems much more slow paced. I'm not so sure whether it's a natural consequence or if it just happened to become this way and continues to be so because we expect it.