I should probably post my answer. Maybe it's because my first episode was the Joe Don Baker western (I forget the name. Final Justice maybe?), but I've always been a Mike guy too. I just always laugh harder when Mike is tearing a movie apart. The mean streak is what makes the mediocre Mike movies better than some of the slogs we got in the Joel seasons.
The real debate is who makes for a better Crow? Trace Beauliu or Bill Corbet? Mike, Bill, and Kevin make for such the perfect dream team that I can't go back past season 8 anymore. I've been to see several of their live Rifftrax broadcasts in theaters and those guys are still incredible together.
While I think both of them were great in their role, I've always preferred Mike slightly more. Joel always came across as uncomfortable in front of the camera whereas it seemed more natural to Mike. I also felt that the relationship between Mike and the robots was better. If you're taking modern stuff into account, then it would easily have to be Mike. Rifftrax is much better than Cinematic Titanic. Despite all the talent involved with Cinematic Titanic, they just don't have the chemistry or timing that Mike, Bill, and Kevin have.
Joel is amazing his sleepy delivery and friendly nature is very suthing and gives that much more power to more cynical jokes when those come up. I grew to like mike but most of his stuff is in the later seasons where the out of movie segments grew unbearable. Both still hold up though, even the early pre-comedy central stuff.
Always, always Mike. Like others have already said, i liked Mikes' s snarkier delivery better, the movies of Mike's era were better and better for riffing.
Pretty sure Mike was one of the main writers for the show from fairly early on so the debate is a little moot. It was always Mike's words in Joel's mouth! :)
I think which one is better depends on which movie they happen to be riffing on (ditto on comedy in general-- I think you're generally only as good as the content you have to work with). I find the riff generally funnier if the movie itself is hilariously bad instead of just boringly bad.
That being sad, my favorite episodes are Santa vs. The Martians, Space Mutiny, The Final Sacrifice, and Pumaman.
Ask the internet, and ten times out of ten the majority will favor everything seasons 8-10 of MST3K, than anything before. The series speaks to this generation by being more cynical and mean spirited (in both their treatment of the films, and towards each other in the host segments.) Trolls on 4chan, something awful reviews, youtube videos of people screaming at bad videogames... the internet loves to be angry. That just can't compete with Joel's "Lemons into lemonade" approach to the series where he was trying to make fun out of the movies, rather than making fun of them.
That being said. Joel. He's the daddy. The show certainly was a lot funnier in the last three seasons, but not just because of Mike (keep in mind, he was the head writer of the show when Joel was around). Bill played a much more charismatic Crow than Trace ever did. They got the rights to a lot more 70s and 80s movies (even a few from the 90s), which are bad in much more entertaining ways than the 50s-60s ones Joel had to work with. And the planet hopping + clean slate of bad guys brought a lot of fresh ideas to the usually dull and formulaic host segments).