PDory, welcome to the "other side".
I don't have a trawler, but I have a 28' commercial crabber (think big-11000lb-runabout) with a 200 hp diesel and sterndrive that we use to commute back and forth from an island and a 34' pilothouse sailboat, so I have some basis for comparison in order to answer your question.
The things that I feel are about the same cost are: electronics (you can spend as much as you want with either), haulouts for bottom paint, zincs, etc.(about once a year- I haul out more often because of sterndrive services), general maintenance (buffing, waxing, galley repairs, head, etc), moorage(if the same length),insurance(?).
Sailboats are gear intensive and so a lot of sailors (mostly racers) have to have all the latest and greatest gear available which all costs a fortune. Even if you are not a gearhead, we all manage to find a few things each year that we can't sail without. There is a lot more equipment on a sailboat to wear out, from lines to winches, standing and running rigging, and let's not forget sails. This all adds up over the years. Of course, a lot depends on the size, age and type of sailboat you have. I would be hard pressed to put a dollar figure per year on this for my 34' pilothouse, and my costs wouldn't be representative because it has been a total restoration.
The obvious big expense of the power boat is fuel, you don't move without it, so every hour you can multiply the GPH by the current cost of diesel. In my case it is 7GPH for power, 3/4 GPH for sail when I am motoring which is for sake of argument let's say 50% of the time. We can all do the math(power-ouch!). The big difference I think most people don't think about is that because of the cost of fuel, most powerboaters only run the boat when necessary and in a straight line toward the destination. In other words, they don't run it anymore than absolutely necessary. I am talking about liveaboards and full time cruisers, not the two week vacation. So I think the powerboater, especially someone that is retired on a fixed income will be inclined to not run the boat nearly as much as a sailboat which can be taken out at most times for practically nothing. So not only is the sailboat cheaper from a purely financial aspect, but also more rewarding in all respects because you tend to use it more often, which after all, is the whole point of spending the rest of your life(or as much as possible) on a boat.
In my case, I know I spend a lot more per year overall on the powerboat, primarily because of fuel, but also engine maintenance. The other cost that will end up biting me is the cost of engine replacement which I figure is somewhere between 8-10 dollars per hour (which is probably twice what a trawler would be). That is a cost the broker will never mention and most owners choose to ignore, but it's a fact that you will put a lot more hours on a powerboats engine than a sailboats, and the cost difference is huge between a 30-50HP engine and one of several hundred HP.
IMHO the answer to your question is yes, it will be considerably less expensive to liveaboard and cruise on a sailboat than a trawler. Sorry for the long winded answer, it was a good mental exercise for me to go through all of it for myself as well.
SV Laurie Anne
1988 Brewer 40 Pilothouse