In the arcade version you get less lives and bombs, which means that you get less points for the end-of-stage bonus. The score calculation for lives and bombs is:
(lives * 40,000,000 + bombs * 20,000,000) * difficulty
The difficulty multiplier is 1.5 for Extra mode.
So assuming you NBMB (which you're ideally supposed to do aside from one bomb at the very beginning), then the score bonus from lives and bombs should be:
- Arcade - 4 lives 8 bombs = (4 * 40,000,000 + 8 * 20,000,000) * 1.5 = 480,000,000 points
- PC - 10 lives 10 bombs = (10 * 40,000,000 + 8 * 20,000,000) * 1.5 = 900,000,000 points
So PC earns an extra 420,000,000 points.
It's worth pointing out I don't actually know a lot about the arcade version, so there may be other differences I'm not aware of. I've played it a tiny bit and it didn't seem particularly different, but I haven't done any side-by-side comparisons. I also haven't actually seen any of the high-level Extra mode runs for the arcade version, so I'm operating under the assumption that the routing is fairly similar to what I'm doing.