The two main differences I have seen (and I could be wrong since I use only the default settings), is Disqus alerts you only when your comment is responded too. LiveFyre alerts you via email every time there is a new post on that blog entry. It does this automatically once you comment. I need to check deeper into the settings. And one glaring difference which sets them apart is Disqus allows you to go back and edit your comment, even after posting. LiveFyre does not. This is huge for someone like me who types slower than my brain thinks and often posts with spelling errors. I have not seen a Spell Check Feature on either which is sorely lacking.
I am not sure who the VC backers of Livefyre are, but Disqus is backed by Union Square Ventures which has in their stable, Twitter, Tumblr, Zynga and Boxee among other great Social Start Ups. And @FredWilson who is one of the partners has an amazing blog that is a must read for Entrepreneurs www.avc.com
Long term I see networks like this being integrated across all platforms and websites and I predict they will outlast even Facebook and Twitter for their usefulness!