The Type VII and IX subs were really more like boats that happened to be able to go under water for a while and come back up again. As such, they were designed to operate better on the surface than submerged.
The Type XVIII and XXI on the other hand were designed to be a true submarine; they operated much more efficiently submerged than the previous uboat designs. Hence they could travel faster submerged than the VII and IX.
The most important difference between the XVIII (which was never actually built) and the XXI was the XVIII had large tanks full of H2O2, whereas the XXI used this space for more batteries.
The diesel motors on the XVIII were capable of producing about 4000 - 4400HP, and usable only on the surface. To go full speed submerged with a snorkel on the diesel would rip the snorkel right off.
The Walther turbine, however, generated close to 4x the power of the diesel, about 15,000HP estimated. This engine also had the benefit of working surfaced or submerged. So combine a hull designed to operate under water with a 15,000HP engine... you can see where 25kts might have really been a possibility. Of course, no one knows the true speeds since one was never built.
The XXI relied on the sheer volume of its high-capacity batteries to attain its 17kt+ speeds under water. Obviously the batteries could not generate 15,000HP so it would not have had quite as much thrust underwater as the Walther turbine might have had.
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