I'm not a gun show type of guy, but assuming the dealer is going to charge $350 + tax which totals about $380, then why even consider the dealer and the 4473?
I'd figure in tax and a tiny bit for the hassle of the 4473 and the wait, but beyond that, the paperwork doesn't worry me. I've got so many of 'em out there with my info, plus the NFA stuff, like mentioned above, it doesn't phase me anymore. So, $380 might be ok over $350 from the dealer, but I certainly wouldn't go more, and it's just for my personal hassle and wait time, is all.
I used to think no 4473 sale could bring an extra 20-30 bucks but those days are gone for me. For most gun owners with just a single to small collection the private sale may still bring the extra though.
I guess I'm the odd man out. I'll usually pay a bit more to my LGS. I've known him for years and I know he gives me the best price possible. He also makes me a custom holster for each gun I buy from him if I need it and is willing to handle any issues if it needs to go back to the factory for any reason and is a fellow Mason.
I prefer that over buying from an unknown individual who may or may not be telling the truth. That being said, if I find something I want at a decent price from an individual I'm not opposed to buying from a private individual.
It's too complex a question for a simple answer. If both are used in the same condition ("good" visually, but no REAL information beyond that) I'd expect the private party to be the same or less, "out the door". Guns are such a hot commodity anymore that I assume anyone selling a gun is trying to make money; thus the private guy has less overhead and thus should sell for LESS. Not more.
Prefer a private sale, I don't really like filing the 4473.
Last time I did one was at Academy. Now it's on their electronic tablet. Easy peasy. Never pd a premium...