I'm going with both right. Time is relative.
Right. So how can we assign an age of the universe? Time is relative. It's a different age depending on the frame of reference one calculates the age from.

If I go for a ride in a really cool spaceship at 0.99c today and arrive back in exactly one year (from your pov), then maybe a few minutes or whatever have passed for me, while an entire year has passed for you.

So as we stand next to each other discussing the age of the universe, practically in the same region of spacetime, we have nearly a whole year discrepancy between our values. I say it's 13.7 billion years, you say actually it's 13.70000001 billion. Obviously I'm being silly here because it's not like the 13.7b is supposed to be a precise value. But this just demonstrates that the concept of the universe having an age seems utterly ridiculous as a direct result of relativity. The discrepancy in universal age between us here on Earth and an object orbiting very close to a black hole would be enormous. But, because time is relative, both are right.

This conversation is particularly enjoyable, I must say, even if I'm failing to get my head around this.