Shovelware goes where the most people are. It doesn't matter who the people are either, and it's been this way long before the PS2 or the Wii came along.
Wikipedia (yeah, I know) claims that the PS2 has 2,015 games in its library as of January 2010. It still gets games released today, but they usually aren't high quality ones, and they don't get much coverage. These new games are almost exclusively shovelware.
Of those 2,015, only a fraction would be the good games, the largest chunk would be the average games, and another small fraction would be the bad games (and this is where the shovelware comes in, as it won't be the highly rated games). Metacritic (as imperfect as it can be) has 514 PS2 games rated green, to give you an idea of the ratio of good to average to bad here (So 25.5% of the PS2's library garnered enough praise to be considered good). That still leaves 1,501 games to be split between average and bad. Even if ~1,000 of those were average (which is a pretty high amount to say the least), that still leaves ~500 games which would be bad.
The trouble is you can't use something like Metacritic for the truly bad games, because so many of them don't even get picked up by review sites, thus they can never appear on such a website.
Meanwhile, Wiki also claim the Wii has 962 games as of November 14th. The smaller the total, the smaller the ultimate divisions of good/average/bad will be. It's just pure logic. 170 Wii games have the green rating from Metacritic. That's 17.7%, which isn't that different in the grand scheme of things. Assuming again that the 'average' games have the largest section, you're looking at a similar number of bad Wii games as there are good, if not slightly more.
Given how many games there are left in the PS2's library after taking out the good games, I'd find it hard to believe that there are less than 200 of those that would be the bad ones. Using sheer logic, it has to be the PS2, more down to the fact that it had so many games released for it (and continue to be released for it) rather than anything else.
Ask the question in another few years when the Wii gets closer to the PS2's sheer number of releases, and the outcome might be different, as the Wii just doesn't get as many good games to help balance things out, but that's not a topic for this thread.