If Stats come first, random or not, in order or not, it means that Stats matter. If I roll an 18 in Str or point-buy an 18 in Str it means that I'm good at Strength...-y stuff. It defines my character, sets him apart from those that don't have an 18 in Str. Since Strength is rolled for fighty stuff, taking or rolling an 18 in Strength means my character is fighty. In an extreme case I don't really need anything else than stats here, and could totally play the game just off of those.
If Powers (I'm using a 4E term, but I don't mean 4E specifically) come first, that means Stats don't matter. In fact, in 4E I honestly see little point in stat-differentiation. If you play a specific Role/Class, then you're going to want your best Stats for that Role/Class. If you pick Wizard, just get an 18 in Intelligence and have it over with, classes could totally come pre-packaged with specific stats. Or really, the game could drop stats altogether. If I roll/pick/buy a high Charisma I will play a Sorcerer (or Paladin). If I play a Sorcerer (or Paladin) I will buy/pick a high Charisma.
So in other words - if Stats come first, I don't really need a class. Having a high Strength makes me a "Fighter" by default. If Class/Powers come first, I don't really need stats. Being a Wizard will make me Intelligent by default.
So there you have it. I used extremes as my starting point but the result is sensible I'd say, from an Occam's razor standpoint. Of course you can claim that you'd still need classes because in all-stats characters will be indistinguishable from each other (and thus boring) or that you'd still need stats in an class-first game because otherwise two classes would be indistinguishable from each other and thus bor...stop me if you've heard this before.