It would be better. Old subs COULDN'T stay under very much. New subs hardly ever surface.
A pre-nuclear subs biggest fear was getting caught on the surface by destroyers or planes. Though they practiced 'crash diving' to shave seconds off their time to submerge, those seconds were the difference between safety and being sunk.
Rapid dive time was one of the major reasons the Type VII U boats were comparatively small, at 780 tons and 220 feet. They could dive quickly and the smaller hull cross sections allowed for deeper depths. The Type VII had a test depth of 750 ft and went deeper in combat - around 1000 ft.
Even the larger, longer ranged Type IX U-boat was still small, 1150 tons and 251 ft, by WWII American fleet sub standards. These also had a 750 ft test depth.
The American navy's Gato, Balao and Tench classes were all around 2400 tons and 311 ft. They took a lot longer to dive and the test depths were just 300' for the Gato and 400' for the Balao and Tench classes, although they regularly exceeded that by 150% (450 ft and 600 ft respectively), which was near their crush depth. They were optimized for surface operation with a top speed around 21 kts, and a top speed underwater of around 9 kts for about an hour, or just only 2 kts for a 43 hour endurance.
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Late in the war the Germans developed the snorkel to allow their existing U boats to use their diesel engines underwater, which allowed them stay under water where they were harder to detect visually by air or by radar, although it wasn't fool proof as the feather from the snorkel was still visible and the snorkel still had a small radar signature. It was however uncomfortable for the crew as a large ball valve closed anytime the snorkel was submerged. Consequently in rough seas the snorkel would submerge, the induction valve would close and the diesels would start sucking air out of the interior of the sub, which caused ears to violently pop, etc.
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By the end of the war the Germans were experimenting with much more advanced U-boats. The first was the Type XXIII, which was small at 134 ft and 260 tons. It had a snorkel plus a very large capacity battery. The large battery along with careful attention to under water streamlining made it the first submarine that was faster underwater than on the surface - a common trait in modern submarines. It was short range coastal boat that carried only 2 torpedoes, but it could travel almost 200 nautical miles submerged at 4 kts.
The Type XXI was a larger boat, at 251 feet and 1800 tons. It was also streamlined and faster submerged than surfaces and equipped with a large battery giving it a 340 nautical mile range submerged at 5 kts, able to stay completely under water for 75 hours and then recharge the battery quickly in about 5 hours using the snorkel. The high underwater maximum speed (17 kts) combined with a snorkel allowing it to remain submerged entire patrol made it the only German submarine that truly had a good chance of completing a patrol by 1945.
The few Type XXIs that were completed were highly prized after the war and the Soviet Zulu, Romeo and Whiskey classes were based on them.
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The US Navy applied what was learned from the Type XXI after the war to a number of the Gato, Balao and Tench class submarines under the various Guppy (Greater Underwater Propulsion Power) programs and the Fleet Snorkel program.
The Guppy I and II boats (24 total) converted between 1947 and 1951 used a much higher capacity battery inside a much modified hull to create space for 4 battery wells. The hull was also carefully streamlined and had a new streamlined sail. The improved streamlining along with 2500 hp low speed direct drive motors allowed the Guppy II boats to do 18 kts underwater.
The ten Guppy IA conversions in 1951 were a lower cost conversion without the larger battery, but it used a more efficient battery than the WWII era boats and had more crewe space than the Guppy II boats. There were also 4 Guppy Ib conversions that were done for foreign navies without the upgraded fire control systems.
The 17 Guppy IIa conversions completed between 1952 and 1954 were the same as the Guppy II except one engine was removed to create more room for equipment in the boat and made them more habitable.
The Guppy program's ultimate evolution was the 9 Guppy III submarines converted between 1961 and 1963. These were similar to the Guppy II, but were increased in length to 322 ft to provide more room for the improved sonar and fire control systems including the capability of Mk 45 nuclear torpedoes.
There were also 29 boats that received the low cost Fleet Snorkel conversion between 1947 and 1953 that removed the deck gun, added a snorkel and added a streamlined sail to the boat, while retaining the original battery and deck configuration.
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The US Navy also designed the Tang class fast attack diesel submarines in 1946 and commissioned six boats in the class in 1951 and 1952. These were shorter 268 ft boats with circular cross section hulls and test depth greater than 700 ft. They had a submerged endurance of 43 hours at 3 kts, or 1 hour at 17.5 kts. In 1967 four of the boats in the class were extended in length by 22 ft to 292 ft to provide more room for more advanced fire control equipment. The Tang class was also the pattern for the first eight nuclear submarines in US service in the Nautilus, Seawolf and Skate classes.
The Barbel class was commissioned in 1958-59 and the four boats in the class combined diesel electric technology with the albacore/teardrop shaped hull that became the norm in modern nuclear submarines. These were 220 ft long boats displacing around 2600 tons capable of 25 kts underwater with an operational depth of 700'. They could maintain 25 kts for 90 minutes or 3 kts for 102 hours. The Barbel class tested the hull design in service, while the Nautilus Seawolf and Skate classes tested nuclear propulsion under operational conditions and these boats together were the transition from the diesel to the nuclear submarine. They were also the last diesel electric boats in US Navy service.
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Short version? The US Navy benefited a lot from the late war Type XXI and XXIII U boats and those lessons were integrated in diesel electric boats that remained in service into the 1980s.