We have sailed Eurodam four cruises and I promise you we would not have returned if she didn't 'ride well'.
She's a beautiful ship and we were amazed how much we liked her as we did not expect to. HAL really did a great job with her IMO
Older ships were made differently than the ships made nowdays. Stabilizers really make a difference in the way the ships pitch and roll. Of course, if you get bad weather, you may feel the sea much differently than you would on a calm day. If you get sick, DO NOT remain in your cabin. Go outside if you can, or at least get fresh circulating air in one of the big public rooms. Do not look at the horizon and try to bring some medication with you (Transderm scope, Dramamine, Bonine, some ginger tablets) just in case. I fill up with bread/crackers/rice/pretzels and go easy on the liquids, although you need to keep hydrated.
Good luck and don't even think about instability--just enjoy your cruise!