Good question, but complex to answer precisely.
Short answer: same order of magnitude for four people.
Longer answer:
The airplane burns about $75 of gas & oil per hour, and I figure the total cost is about $250/hr. (I fly it about 125 hours a year, and all my costs, including hangar, charts, insurance, in-year maintenance/inspections, and maintenance reserves for long-lived items [engine, prop, avionics] come to around $30K/year.) My local flight school rents a newer version of my plane for $209/hr, but they fly more hours per year, so that indicates my cost estimates are in the right ballpark.
This trip will be about 15 flight hours, or just under $4K in avg costs, or just over $1K in marginal costs. That's for a family of four (two adults, two kids 2 or over, so everyone needs an airline seat).
In real terms, if we had to fly commercial, we'd have skipped seeing my very old grandparents (always possibly for the last time), and only flown into Lexington for the wedding, rented a car for the week at the lake, and driven the three hours down here like the rest of the family.
Looking at far advance purchases on hipmunk, that looks to be $484pp on Delta, plus $100 in bag fees (2 bags, round trip), plus a rental car that we can avoid by having one of the family cars pick us up at the small airport just down the road from the lake.
So, same order of magnitude: airline is more expensive than the marginal costs, less expensive than the average costs. (And there's a lot of "hobby time" to train, stay proficient, geek out on airplane forums, and light airplanes are not nearly as "almost all weather" as airliners.)
Other less tangible items:
Much safer statistically to fly Delta than a piston single.
My kids know "Jeda and Baba", their late 80s great-grandparents, because they live 2 miles from a cheap-gas airport on the way to/from one set of their grand-parents, so we stop in for lunch/dinner and sometimes one overnight on those trips, including this one. I'm not especially sentimental, or extended-family oriented, but even still, that's worth a lot to me, as the day is coming all too soon when they won't be here and if we flew commercial, we'd literally never stop in to see them except for family funerals.
Big one for my wife: my airplane has lavatories at "either end of the flight", but not on-board. Now, we can divert anytime and be on the ground inside of 10 minutes usually, but for a 2 or 4 year old, or a pregnant 30-something, that can be a long time...