You say you were hit "out of nowhere" last Friday; however, there was a perfect storm of both Air Traffic Control slow downs due to the shutdown AND the fact that Friday saw thunderstorms (always the wild card at DFW). Here's a CNN piece regarding the ATC issues. Some background on weather issues last week as well. While the shutdown is likely to be over by the end of the year (assuming they don't just keep putting stop-gap measures in place that expire, etc.), weather will be your concern. While PHL is more likely to have serious weather in the sense of snow, ice, and blizzards, a single thunderstorm at DFW can strangle airport ops for hours, and if your plane is in the vice... you know how it goes.

If it were me, I probably would not risk spending NYE in an airport--not if I had plans that mattered. Remember, the airline will owe you nothing if WX is the delay.

I also prefer PHL these days--but that may be the fact that DFW was my home airport for two decades and is still my work airport. So that's innate bias against the familiar. When DFW is good, it is very very good--but when it is bad...

Keep in mind, PHL has better access to other airports within the allotted radius if you have a cancellation. NYC airports are within semi-accessible traveling distance, and if flights are canceled, all airlines allow rebooking, but the flights fill fast. With four of you, space is even harder to come by. DFW is not close to any other major airport. Austin, IAH, or OKC are closest, or OKC, but those are still not AA hub airports.

If you are planning for contingency (if it's that important, book the day early from PHL). By the time it's travel time, you wil know early enough if a blizzard is coming and a weather waiver will likely be issued so you can proactively rebook. This is not common with thunderstorms. Last December, there were several days of thunderstorms in the DFW area. I remember how "irritated" I was because it seemed never ending (like who was I actually irritated AT? So silly!)

In the end, the extra day could save you a lot of headaches. And if nothing goes wrong, you will enjoy an extra day and a lounge at PHL (PE gets at least the AC, yes? The new one is very nice, as is the Flagship.)