Lots of this answer can ultimately come down to the different natures/requirements of submarine warfare in the two conflicts, but there were some big differences in submarine design (although many similarities as well). Many of these differences are explained by general technical progression, as well as the fact that WW1 was the first large-scale submarine operation, and during that time it sometimes wasn't clear how submarines should have been built
Powerplants and Fuel Efficiency: Early in WW1, several different engine and fuel types were used aboard submarine. Paraffin/kerosene powered engines were common early on, and had some big drawbacks (smelly/foul to work with, smoky, etc). Diesel then became established as the best choice. By the time of WW2, this choice had become the default so there wasn't much in the way of experimentation, although by then the engines were more powerful and fuel efficient because of the natural progression of technology (3200 hp for a WW2 Type VIIC vs 2400 hp for a WW1 Type U-87). Battery and electrical technology also improved between the wars, though the general idea was the same.
Torpedo Technology: In WW1, you were pretty much stuck with steam torpedoes. WW2 introduced wake-less electric torpedoes, magnetic fuses instead of just impact, better and more reliable gyro angle and direction keeping, pattern-running torpedoes (which could turn and follow a sort of ladder track after a preset distance to keep recrossing the target path to improve the odds of a hit), and even acoustic homing torpedoes. Also, the aiming methods improved; by WW2, the work of the weapons officer could be transferred from paper/pencil/slide rule to an analogue computer.
Construction Practices: The advent of welding and other construction techniques/better materials made a huge difference in the underwater capabilities of the submarines. If we again compare the two ocean-going workhorses, the Type VIIC and the Type U-87, the VIIC had maximum operational depth of around 220 meters, while most WW1 types were limited to around 50 before rivets began to pop.
Those are the principal differences between the submarines themselves. There are other factors which correlate more to the environment they operated in (such as AA weapons and more of them on WW2 submarines, radar warning / electronic warfare devices, but those differences are pretty much common to all ships of the two wars rather than just submarines.