I fly out of EWR regularly on business and always park my car in the on-site economy lot ($10 per day) and take the free shuttle bus to the terminals and have never had a problem. Conversely we used Avistar once 2 years ago and it took forever for them to pick us up when we returned, and then my car had a new scratch in it which they were very unapologetic for.
Obviously my experience does not mean that one is inherently better than the other, but just don't automatically assume that off-site is better, safer, cheaper or faster.