I've seen both. Had exactly the same impression: it looked like Tornado was a cheap knock-off of Twister, but I sort of remember they came out at about the same time. There was some pre-release media hype about two competing movies on the same topic being under development, and speculation about which one would be the better movie. Twister won, hands down!
(Actually, I think some of the cheesy lines are part of what makes the movie appealing, in a juvenile sort of way. The guy who talks about "the suck zone" and "imminent rue-age" is a great geek portrayal. I knew plenty of guys just like that at Harvey Mudd college; just naturally "cheesy"!)
It wasn't the first time that has happened. There were two volcano movies ("Dante's Peak" and "Volcano") whose production schedules overlapped, which also benefited from similar pre-release hype about the competition between them. They turned out to be quite different movies; much less similar than the tornado-themed movies were.