This is a difficult question since the Germans and the Americans were operating under very different conditions. To a large extent, each side built the boats they needed, but overall, the Germans were the better mechanical engineers and had the more efficient designs. For example the American Diesel electric drive was quite inefficient in weight and use of space, but it was more robust than the German Diesel direct drive. The Germans only used Diesel electric drive on the Type IX D2, which was interestingly about the same size as a US fleet submarine, and there was a hybrid Diesel direct / Diesel electric drive on the XXI.

The diving performance of the U-boats was largely due to advanced welding techniques and superior welding quality. BTW, you overrate the diving performance of the Type XXI, it was essentially equal to the later VII C boats. The XXI did not meet its original design goals, which is not surprising when you look at the conditions under which it was built.

The really good diving performance was supposed to be by the VII C 42 design which used armor plate (28 mm of CM 351 alloy) and had a design depth of 200 meters, maximum safe depth of 300 meters and a crush depth of 500 meters. Several U-boats of this design were ordered (U-1069-1080, U-1435-1439), but the project was stopped in October 1943 in favor of the XXI.

When you bring radar and sonar into the picture, you are no longer talking about submarines, but about electronics, but as you say, the Allies were ahead in microwave radar and the Germans probably pulled ahead in sonar, but it is difficult to get detailed specifications on late war sonar from both sides. The XXI was certainly able to torpedo a ship without seeing it.

Regards,
SuperKraut