Well, then it's obviously not a minion! In fact, a level 35 minion is worth 11,750 XP; compare to the level 19 solo: 12,000 XP. So, XP-wise (and hence power-wise) they're roughly equivalent - meaning the level 1 character would see the Daikaiju Citystomper as a level 19 solo.
Or as a level 24 elite. Or a level 27 normal monster. Depending on your level.
Only characters in the level 35 region would treat it as minion.
Cheers, LT.
Ah, but I don't believe that. Those statblocks aren't in MM4. There's the Daikaiju Citystomper Minion, L35, and there's the Daikaiju Nukelizard (Level 38 Solo Artillery). And there's the Daikaiju Hatchling (Level 10 Elite Brute). And that's it... that's all there is. Those Level 19s and 24s and 27s you mentioned aren't in there.
I was just being funny with the example, but I've actually heard this "minions are relative" argument repeated often. I think people say it a lot but I don't think it actually has anything to do with 4e. I'm not saying you're putting me on... but think about it. What happens to the Level 19 Flumph Marquis when the PCs are Level 29. Does he become the Level 6 Flumph Bravo Minion? No... he's not a Bravo, he's a Marquis. And he's not Level 6, he's Level 19. And some monster entries don't even have minions.