Keep in mind if you're selling to new customers, they may find your web app "dated". The new customers likely won't compare the web app to your desktop app, but to other competitors web apps. And these days the expectation for better or worse is that web apps look and feel a certain way (favor whitespace). I'm sure a dense UI can still look clean and modern, but it will take more effort.
We actually got some ex-graphic designers on our team now, so at least there won't be any more "programmer art" icons and such.
Fortunately our customers are mostly interested in functionality, and there's not a ton of competition. But yeah, a good looking interface does have a distinct impact so it will be something we'll have to balance.