Beside party sizes, the dungeons are also different.
There are 3 levels for regular dungeon:
Unknown – Dungeon Basement level 1 (Difficulty Normal): This is currently in development and not available in the game.
Crypt – Dungeon Basement level 2 (Difficulty Hard): This level is currently the starting level for the normal dungeon.
Inferno – Dungeon Basement level 3 (Difficulty Hell): This level is only available through surviving and entering red portals.
Ruins – Dungeon Basement level ? (Difficulty Normal): This level is currently the starting level for the normal dungeon.
High Roller Dungeon: These dungeons are higher difficulty versions of the regular dungeons and will have higher quality loot. Every single enemy will be elite or higher.
There is only 1 level for solo dungeon:
Goblin Cave – This dungeon is solo only that has their own ores, bosses, and enemies.