All of which is merely background information to ask if I am going to need to have flat calm Gulf waters to come across, or if a trawler can take reasonably rough water without all that much discomfort?
John
To answer your original question, most cruisers of the type most of us have will take rough water better than the people on board them.
If you have a cruiser with a semi-planing hull it will have a shorter, faster roll with a sometimes very abrupt snap-back when it starts rolling back the other way. As opposed to a displacement hull (there is no such thing as a "full displacement" hull-- displacement is like dead; you either are or you aren't) which has a longer but slower roll with (usually) a more gentle transition to the roll back.
Some people find the snap-back roll of a semi-planing hull uncomfortable, some people find the slower, longer roll of a displacement hull sickening. So you have to pick your poison using your own preferences.
But as long as your boat is designed and loaded properly it will most likely be able to take whatever you can.
The other issue with most of the cruisers most of us have is the transom. Boats like our GB have wide butts. This is to maximize the volume of usable space inside the boat for things like queen berths and such.
In a following or quartering following sea, if you have a slow boat like ours the waves will be overtaking the boat, and when they encounter that big, flat transom they will shove the back of the boat around with all the power that waves pack with them. Keeping the boat from being pushed around broadside to the waves, or worse, being slewed around violently into a capsize (broach) can require some lively and continuous exertion with the wheel and sometimes the throttle(s).
Autopilots can help but the situation can reach a point where an autopilot can't keep up. Also, an autopilot can't anticipate, it can only react. The last fourteen years have taught us by virtue having to cross five to seven miles of an often-rough bay at the beginning and end of every run that handling a boat like ours in rougher water with the waves behind us requires as much if not more judgement, anticipation, and before-the-fact action with the wheel that reaction with the wheel when each wave hits us. And an autopilot can't do this.
So the bottom line is that I think cruisers like ours can handle a hell of a lot in terms of rough water. The more relevant question is what can you handle? What kind of a ride are you most comfortable with, and how good are you-- or do you think you can become-- at steering a wide-ass boat in conditions that are trying to take control away from you?