It really rustles my jimmies when people use that expression. What does it even mean? If anyone is a more complete footballer, it's Messi. Messi can play on the wing, as a true or false 9, as a classic 10, and probably anywhere in midfield. I could see him even doing fairly well in a Pirlo deep lying midfield role because he has great control, vision and passing. It's just an underrated asset of his in comparison to his finishing and dribbling.
Ronaldo may seem annoying and full of himself but I respect his abilities. He is a fantastic footballer. However, he just does not even come close to Messi in terms of overall play. I cannot bring myself to believe that there are ACTUALLY people who think that because Ronaldo is taller and gets more headed goals plus scores the occasional long shot; that makes him the more "complete player". He could never be as successful in any type of midfield role. From what I understand, he doesn't even like playing as a true forward because he doesn't get to use his speed to gallop down the wings.
I agree with everything you are saying. In one sense, Messi is actually far more complete. When people say Ronaldo is more complete, it is as a scorer. In that sense, yeah, he is more complete. He makes more header goals, has longer range, etc. In my mind, this is a red herring though. People are basically saying "Ronaldo can score in more ways than Messi, so he is a better scorer even though he doesn't score as many goals." When you take this argument to its extreme, it shows its absurdity. If there were one player who scored 10 goals, each of a different type, and another who scored 85 goals, each of the exact same type, there is NO WAY anyone would say the 10 goal player is a better goalscorer. Is he more "complete" a goalscorer? Yeah, probably. He can score in ways the other guy can't. But the other guy is SOOO much better at the one way that he does score, that he's clearly the better goalscorer.
The same is true of Messi and Ronaldo. Ronaldo scores in a greater variety of ways. But Messi scores more. All this means is that Ronaldo can score in more ways but Messi is so much better than Ronaldo at the ways that he does score that Messi is the better goalscorer still.
What is similarly absurd is people who try to compare Ronaldo and Messi category by category. They say things like this:
"Heading: Ronaldo
Long Range Goals: Ronaldo
Free Kicks: Ronaldo
Dribbling: Messi
Passing: Messi
Ronaldo wins more categories and so he is better."
This argument is just absurd. People who do this are taking very minor skills (such as heading) and elevating them to the same level as very major skills (such as dribbling). If two players are otherwise equal but one is far better at heading and the other is far better at dribbling, I'd bet a whole lot that the dribbling player is the better player, instead of the two of them being even like this method would indicate. The things that Messi is better at are much more important than the different random ways that Ronaldo scores a handful of goals each season.
The argument is also absurd because it doesn't take into account the degree to which one player is better than the other at a given thing. Let's say there are 10 important attributes for a player, and one of them is speed. Let's say we have Player A and Player B. Player A is REALLY SLIGHTLY better than Player B at all the attributes except speed. Player B is as fast as Usain Bolt, while Player A runs a 20 second 100m. If you equated all attributes the same, you'd say Player A is clearly the better player since he is better at 9 of the 10 important things. However, having Usain Bolt speed instead of 20 second 100m speed would EASILY outweigh being SLIGHTLY worse at 9 other things. Again, we see this with Messi and Ronaldo comparisons. Messi is a FAR better dribbler and a FAR better passer. A lot of Ronaldo's advantages in various things are quite small. To equate Messi's big advantage in passing with Ronaldo's small advantage in free kicks (which is probably not even an advantage anymore) is patently absurd.