It's going to be really interesting to see how the two versions of Dragon Quest XI perform. I don't think there's any chance the PS4 version will outsell the 3DS version, but I guess we'll find out soon enough!
It will be a close call I think. Sure, 3ds has a bigger install base, but the PS4 has a very engaged base with a great software attach rate.
This is coming from an unabashed Nintendo fanboy.
Then again, I can see a lot of people buying both versions because of the enormous differences between the two, and one shouldn't underestimate the portable factor. I think 3DS will end up on top, but that's mostly got to do with the larger install base and the fact that the 3DS has seen outstanding support from the franchise. So far, Japan has gotten like 9 Dragon Quest games (DQ7, 8, 10, 11, Monsters 1 & 2 remakes, Monsters Joker 3, Slime 3, Theatrhythm), so I think the system has a devoted fanbase way bigger than that of the PS4.