I've run B3 under at least 3 different rule sets (Basic, 3e and 4e) and I think that it's a great adventure, but there are some caveats. One thing that Zardnarr doesn't get into is that the two versions of this adventure are very different. When TSR recalled the adventure and pulped it, they didn't just fix the one piece of "objectionable" art in it - they got rid of a number of art pieces. The maps were redrawn (mostly the lower level, IIRC) and Tom Moldvay put in a substantial re-write of the adventure - all of the wilderness encounters around the Palace were cut and replaced with a "programmed" introduction for new DMs where you'd read through numbered boxes based on the choices the PCs made. The story was pretty radically changed as well - in the original version, the Palace was in ruins and IIRC the disaster that had struck it was an old one (or at least was some unspecified time in the past). The PCs were assumed to be treasure hunters lured to location by legends of the treasures still assumed to be somewhere in the ruins and the whole thing is a typical dungeon crawl with a fairy-tale backstory. In the re-write, the disaster that had struck the princess was recent, and the PCs were specifically brought to the palace by a race of (fey?) beings known as the Protectors who have put them on a timetable to undo the disaster and stop a mad god-like being from getting out into the world. Plus Moldvay's version had the same "you're trapped in the dungeon and can't get out until you finish the adventure" characteristic that some of Moldvay's other adventures have (notably X2 where the mist surrounding Castle Amber forces you to work your way through the mansion, though it feels more organic there than here, as does the desert that forces your choices in his B4 adventure). The two versions share a lot of overlap, but if you changed the names of the NPCs involved you might be able to get away with running them both for the same group without them realizing it because they give very different experiences IMO.
Over time, as much as I've always liked Moldvay's work, I've come to appreciate the original Jean Wells (orange cover) adventure more and more. The last time I ran it (4e) I used bits and pieces of both versions in my conversion. The next time I run it I might just use the Wells version as is. (The wilderness around the Wells version is strange as well. It might make a good fit for a Gamma World game, or at least a D&D game that is more Thundarr the Barbarian than Tolkien inspired).