If the site did not have www, most people assumed it is probably made by kids, who do not have www yet. See, most people do not understand that www is not a domain like .com which you have to buy. So for average joe consumer, it signals strength. For an enterprise customer, it probably does too. So unless your product is for savvy users or zen-like designers, I'd stick with www.
A lot of people think that naked domain is cleaner. It is actually not, since the average mind is conditioned to read www.x.com, and you have https://x.com. It's cleaner in the sense that a face is cleaner without a nose.