United Kingdom
Slings are better than prams for babies. Even if it's a mud-fest, you can still feel some of the independence, mobility and excitement that you felt pre-kids, plus your baby will almost certainly sleep no matter what. As long as you remember their ear plugs you can even get in the throng a bit (not too drunk mind!)
Prams are what you need for a toddler. You're less mobile, but the good news is you can stash a box of wine, glasses, and camping chairs underneath. You won't have the same sense of freedom as with a sling, so you need a bunch of friends to find a patch with and claim it as your own.
Other tips:
Look for a small festival. With small kids it's more about the experience and the people-watching than the line-up. If you're too determined to prove to yourself that you're still hip and free, you might end up out of your depth at a manic festival, feeling more down-trodden and left-behind than ever.
Festivals that are known for being 'family friendly' might just be a big pram-fest. (Green Man 2007?) Similarly, avoid a festival that has grown very quickly. Finally, choose something that is within two hours of home. Just knowing you can get home if needed might stop you feeling trapped in a sea of mud and mucky nappies.