Personally, I prefer thicker soap, so if I was your customer, the thicker the better. I have always preferred larger sized bars of soap. The only time I want smaller bars is for traveling and for hand washing. But for bathing, I prefer big chunky soap.
I know this is not what you are asking, but there is a way to determine how much your net weight will be. Marie Gale wrote a very useful 2-part article that gives two effective methods for doing so:
https://www.mariegale.com/calculating-net-weight-soap-part-1/
https://www.mariegale.com/calculating-net-weight-soap-part-2/
It may help you to choose the width or you cut, if you have a general idea of the net weight of your bars after the cut.
What are you using now to cut your bars? Do you already have a single bar cutter? Or do you use a knife or bench scraper? Either way, it may help in your decision making process, to weigh a bar that is 1" thick and another that is 1.25" thick, then weigh each of them (new, right after the cut.) Then do the calculation of what the net weight will be using the
Weight Loss from Water Evaporation method in part 2 from the above link. That will not tell you the final width, but it will give you an idea of your net weight for your bars for the two width options.