DS has both. Now he's a Lego fanatic the Duplo is rarely used, but he'll occasionally get it out for a bit. He can follow most Lego instructions totally by himself now (likes to have us there the first time, and he always recognises when he's stuck so can ask a specific question about what he needs help with) and loves that they're more complex than Duplo. Separating the pieces can be tricky, but a separator helps. But, he's got 'that' kind of brain...iykwim.

If you're after something independent, then Duplo would be good (and you don't have to worry so much about keeping it away from the 1yo). As BG said, you could also try the Young Builders Lego as it doesn't have the small fiddly bits.