The ships in question are only as good as the crews that manned them. German submariners had quite a bit more experience in the world of submarine warfare, dating back to the first World War. On average, the officers and crew of the Kriegsmarine were more experienced than the typical US Naval sailor. This was true until the losess suffered by Germany forced her to put inexperienced officers and crews out to sea, to replace their staggering casualties in the Atlantic.
The main weapon of any submarine is its torpedos. The American Balao had 24 while the IX only had 22. The Balao had 6 tubes forward and 4 aft, while the German sub only had 4 forward and 2 aft. Simply put, the American could put more fish in the water and run a greater chance of a hit than the German.
The American sub is faster, 20 knots surfaced, versus 18 knots for the German. Submerged it wins again with 8.75 knots versus 7.7. Speed was critical with any submarine as it allowed the subs to escape escort vehicles and catch up to merchant convoys.
A good majority of the survivability of subs was how deep it could go (to escape depth charges, sonar detection etc) and the German wins this one hands down: 750 feet versus 400 for the Balao.
The deck guns for both subs are similar, the American mounting a 4inch 102 mm versus the German 105. While both had variations on range and velocity, both performed their jobs as they were intended to, put holes in ships.
The American sub put out over 5,400 hp versus 4,400 for the German.
I would sadly have to put my money on the IX. She had superior torpedos, better depth rating and better engineering for her equipment. The American was able to go faster, but weighed near 400 tons more than the German. The German could withstand more days at sea without refueling and resupply but that would eventually hinder the German as the American could refit and rearm with more bases away from the homeland. (even though the Germans had subs called "milk cows" that would refit subs at sea)