The OEM tires are pretty stiff. The height you will gain by going up a size isn't really going to make a difference. Buy a premium tire and it will. I run Continental TrueContact on all of my Subarus. They perform very well in the snow (if that's an issue for you) and handle pretty well for a touring tire. They are, in my opinion, the best all season tire around. Our Forester spends a lot of time off-road on rocky trails, in the mud, etc. The tires have never failed us (on our third set on that vehicle). They ride very well and are very quiet.
Check your tire pressure as well, shops are notorious for over inflating. A couple PSI will make a huge difference.