Whichever one is objectively correct based on empirical evidence.
Fun fact: time travel does exist, and I am myself a time traveler. The fact that I'm travelling at one second per second along with everyone else is just a minor detail.
Imagine if someone just naturally traveled through time at like... 1.0005 seconds per second... What would that look like? Would we be able to tell? Would they be able to tell? Would their perception be different?
This is a Relativity thing, isn't it? Like the astronaut twins sort of...
That's exactly like being a bit closer to the bottom of a steep gravity well.
Yes, we could tell if they took a precise clock with them. In fact, we have to account for an even smaller discrepancy in order for GPS to work: we here stuck further down in Earth's gravity well travel through time and extra ten milliseconds or so per year vs. an orbiting satellite.
Are we traveling through time? Or is time simply a universal constant of entropy? Everything you experience is energy flowing from a higher potential to a lower potential, with some "loss" to heat. Without that downward shuffle, a rock balanced on it's tip is indistinguishable from a time-stopped version of itself.
Basically, time is your body's sensation of the inevitable terror that is the heatdeath of the universe.