Q2 is based on the older A3 8v (golf mk7) chassis and as such shared a lot of components including the interior with the A3 8v that's why it looks more dated.
Where's as the A3 you're looking at will be the more up to date generation (8y).
Unless you're desperate for an SUV I'd go for the A3 as it's a newer design and more up to date. I've been in the q2 and it is just a jacked up A3. No extra room etc. Plus the q2 goes out of production this year. The only other benefit of the q2 is exclusivity as it's been a poor seller.