For those who get compensated for them, a national holiday is a nice gift. For Shuls they create a little blip, since they have to decide whether to go with the regular schedule, switch to a Sunday Schedule, or some other permutation.
The switch to Sunday schedule seems like a logical move, since most people are off and they like to celebrate with a little more sleep. Even in neighborhoods with many minyanim, people generally prefer praying with the home shul advantage, so accommodating them with a schedule change makes sense.
Following the lead of many Yeshivas, some Shuls prefer not to acknowledge national holidays and keep to their regular schedule.
All things considered, it’s probably slightly better halachically to go with earlier times, although in the winter, when some Shuls daven before sunrise to accommodate working people, the later times would be better.
If you’re a getting things done type of guy, you might prefer the earlier weekday times, so you can get a productivity jump on your day.
Many Shuls daven a little slower on Sundays so that might sway a preference one way or another.
If your Shul can fill all the minyanim, adding an extra later minyan might make sense.
In any case, it’s a good opportunity to perhaps get there a little before the start time, daven a little slower, and stay for the whole thing if that’s not your usual practice.
I think a good compromise if the national holiday in question is December 25 is for a shul to daven neitz. That is approx 20-25 minutes before sunrise so that one says shemona esrai at sunrise.
This way, one does not appear to be celebrating their holiday by davening at 8am or later, but also one does not “cut off his nose to spite his face” by davening too early. Davening at 6:30 when surise is 7:30 might be ok if one has to get to work or catch a plane, but is not ideal.
For smaller shuls, that may have only one minyan each day, they should poll the members of the minyan to see which time they prefer. It makes no sense to be shtark and insist on a 6:30 start when no one is working and just drive people to go to another shul with a later start time. It would be even worse if it causes a loss of a minyan.
[I have actually seen this happen in a smaller shul where the Rabbi refused to allow a later time on Dec 25. Only 6 people came to the 6:30 minyan as most just davened later at another shul. The shul usually gets 15 people on weekdays.]
For larger shuls with multiple minyanim, you may see a schedule like this:
Sun 7:00, 7:45, 8:30
M/Th 6:15, 6:45, 7:15, 8:15
TWF 6:30, 7:00, 7:30, 8:15
In many larger shuls, there are earlier and later davening times every day. The earliest weekay times are generally earlier than the earliest Sunday times. The latest Sunday times are generally later than the latest weekday times. It seems that just going to a weekday schedule would be the easiest here, as it still accommodates those who have to work and provides a reasonably late minyan for those who want to sleep in.
So, in summary, a shul with 3 or more minaynim should generally use a weekday schedule. A smaller shul with 1 or 2 minyanim should generally serve the minyanim that have demand.