Now that my kids are school age I am all about having their birthdays at a location. Entertaining kids, not toddlers, is hard work! Two hours at a party space and I don't have to clean my house before and after - sold!!
We've done both, and for me it depends on the age/gender of the bday kid. I love planning at home parties for my little ones (and even my 5th grade daughter), but you couldn't pay me enough to entertain a bunch of 12 yr old boys at our house for my older son's bday, lol! As my big kids get older, we've moved away from traditional bday parties, and onto special bday outings where they can invite a few close friends to do something fun/special together.
I used to do parties at home when the kids were young and I really enjoyed all the planning and decorating as well, but now that my boys are older it's much easier to find a venue to host the party and keep them busy. I'm hoping to move on to inviting a few friends for a special event or activity.
We do home birthdays parties as our kids are still at preschool! And kids enjoy decorating and preparing for their friends arrival. We also make sure to put a birthday banner on the bedroom door which is the favorite part for the kids!