OK boys I've done a careful side-by-side comparison of my US-version of DUNE II with the EU-version.
Other than the box cover, disk aesthetics and paper manual differences noted above, there are only a couple of extremely small differences that I can find. And, I think some of what I discovered should surprise no one.
The Analysis
99.9% of all of the code, graphics and sound that originated in the US in NTSC format were not changed - at all - for the EU release.
With two small exceptions: the most obvious being the title screen.
Since the US version is subtitled "Building a Dynasty" and the EU version is titled "Battle for Arrakis" you see that reflected in each version's intro.

- US title screen, which is also what DOS users saw.

- European title screen
Also, I noticed on Disk 1 (out of 5) that one English game file was ever so slightly different. I believe this is because I think it is possible the US version used North American English where the EU version probably used UK English. In other words, there might be a rare instance where they changed "color" to "colour" and so on.

- Only 3 bytes difference! And you thought ugly Americans didn't care. ;)
The only other change I saw was between the two paper Amiga addendums to the manuals. These single sheets of paper were placed in each box to tell customers how to load and/or install the games.
The US version is completely lacking in how to install the game to hard drive except in the bizarre use case for A600 users with HDDs. The normal installation routine is not mentioned. But in the EU's sheet (written entirely in English) it does explain how to use the Install program on the disk from within the CLI. The US version also has this program (and it worked great) but why it was left off the paperwork is kind of a sad mistake.
Other than that, everything is 100% identical. To that point, the US version also provides the ability to install the game in French or German - just like the EU version! And, of course, all of the graphics are designed in NTSC resolution and look fantastic. I suppose most folks who played this game on Amigas in Europe saw slightly squashed heads and plants but probably didn't really think anything of it.
Before I made these comparisons I used a fantastic CLI program by David Dunklee to create ADFs of each of my disks. Then, I used the physical disks to install the game to my hard drive using the Install program.
Glad I did - because during this process I started to get a read/write error on Disk 1 - the only disk that appears to be unique! Snagged that ADF before any issues so we're free and clear. Phew!
I honestly wasn't sure how much I was expecting things to change across both versions. But I was surprised to find the US-version to be multi-language capable (which the EU disks state very clearly on the disks, and the US disks do not).