I can't speak to OD&D, but I can the others...
Each has a pro-and-con, depending assuming you use the RAW.
Basic is going to focus on speed (combat is quick), exploration, and a lot of "off the grid" problem solving. You'll want to keep treasure high (potions of healing in abundance) and keep the monsters fast and loose (since they are easy to run, feel free to mix it up.) PCs are very frail though, so larger parties have a better bet of survival; make sure they have the room to maneuver.
AD&D (1e and 2e) is going to be deadlier because while the PCs are more powerful than Basic's, the monsters are too. Due to added rules, it slower than Basic, which may drag out play. Otherwise, its the same as above.
3e: Here, we assume things a bit different; a smaller party (4 PCs ave), balanced encounters 60% of the time, and smaller fights that take longer. Also, skills need DCs (spotting doors, opening locks, etc). That said, it is the most through, if not the slowest, dungeon crawl system.
4e: Assumptions change again; 5 PCs ave, bigger rooms (often with terrain features) and heavier emphasis on combat than exploration. Skill DCs vary by target "level", as does monsters used.
Going by that, Basic is great when you want exploration with infrequent, quick fights. AD&D is great for exploring but more detailed combats and traps. 3e is great for very through and balanced combats and exploration (with a lot of prep time) and 4e is great for detailed combats and quick exploration resolution.
Now, how do you want to build your megadungeon.