Well, nothing much different there except for the range. To be honest, if there wasn't that little 200m blip in their reach, I would have been second guessing myself that this was a different ship. So, the main battery is the same as Admiral Hipper's. Dull as this may be, it's a rather good thing. The Admiral Hipper's guns perform well. Their AP can give any ship they slap a big ol' headache. Now, we can't look at the secondary gun compliment because it wasn't from the information pulled from the API data. We can only guess here, but looking at the good ol' Wikipedia entry on the Prinz Eugen, she had the same dual 105mm gun mounts as the lead of her class. We can safely assume they'll be very similar there. I'll list the Admiral Hipper's guns below.
This is a nice little secondary compliment but it's not going to dissuade anyone from getting in too close. That's your torpedoes' job.
This gives the Prinz Eugen 99dps / 233dps / 277dps at ranges of 4.5km / 3.5km / 2.0km respectively. Compare this to the Admiral Hipper and you get 100 / 235 / 288dps at the same ranges. So there we go -- some minor differences! Hooray!
Well, there's no surprise there. The Prinz Eugen gains an extra 30m in the turn and her rudder's 0.2s slower. That's not too bad, really and it's the usual form of "premium tax" that I'm accustomed to seeing.
Verdict: Insert follow-up fat joke here.
Do you feel underwhelmed? I'm feeling underwhelmed. At least, I am on the surface. But this already tells me a lot. The gimmick of the Prinz Eugen isn't going to be found in her baseline stats. I predict that we'll see it in her consumable choice -- at least, that's what the close similarities between the two ships is indicating to me. While the name of the Prinz Eugen would certainly be sufficient enough to make people want to covet it, I strongly suspect that Wargaming is going to incentivize picking up this premium with something interesting.