Regarding Villa/Lampard/Pirlo type signings vs. Maxi type signings - some of this depends upon what is available at the time, and I think there are more choices than just that dichotomy.
The best possible signing is a "Villa" type - a guy who is not yet out of his prime, fits what you want to do, and is strongly internally motivated. But, those don't grow on trees.
Another category is the supremely talented guy that is struggling at a top club - the "Giovinco" type. Similarly, these are available infrequently. Not too many guys like this are willing to come to MLS. Schweinsteiger could be considered one, and it's not clear he will be back next season for Chicago. Chicharito is another, and he hasn't taken the bait.
The third category is the "Maxi" type - guys who are a little younger and a little below the elite, name-brand level, but still good enough to play in a Big 5 European leauge. These have tended to work well: alongside Maxi, think of Piatti, Lodiero, Valeri (lots of Argentines in this category for whatever reason). There are more of these around.
The fourth category are expat Americans who will come home for a big enough check. This one has gotten rather picked clean in the last few years, and returns here appear to be small.
The last category is younger DPs. Guys coming up who view the league as a stepping stone. Atlanta has gone long on this approach and it's worked great. These guys also count less against the salary cap and can bring GAM rewards when/if they are sold. Frankly, Herrera is a guy like this, but we lucked out by not having to count his acquisition costs.
My personal view is that you try to get one "Villa" type, one "Giovinco" type and one younger DP, and if you can't find what you are looking for, get a "Maxi" type.