I think the general consensus is that they're both worth a watch. I'm surprised by those that like one, but find the other unwatchable though. To me, they're 2 different takes on the same theme, but both arguably great approaches.
You don't really get as silly and glitzy as Armaggedon. It's really the precursor to 2012. Over the top action, cool cuts, and an absolutely ridiculous plot. If you watched it in the theater, you very likely walked out with a big grin on your face.
Deep Impact really does a good job exploring the human experience of a more realistic plot. Following the 2 main protagonists through the journey of discovery and rise to celebrity, along with the way they handle the tragedy of having to leave loved ones behind. We also get to look at how a fictitious president would handle the burden of triaging the population of his country, without being allowed to just roll the dice entirely on a world-saving plan. The reality that the plan had a low probability of success, so they had a massive contingency plan in the works. One that as large as it was, couldn't hope to save everyone.
Both are good in their own right.