The only specific benefits is there is a very large positive diplomatic boost, plus a Civ must give its U.N. vote to its most recent liberator.
It's a lot better now than previously; they are much more likely to become friendly, ask for DoF, become a research pact buddy, trading partner, etc.
If you are capturing cities but don't have a lot of happiness to spare, liberating as well as gifting the liberated civ a few conquered cities can get you an ally for a long time.
If you're going domination you can always liberate a non-capitol city (if they had one) if you capture it first