I'm using Linux but I won't consider installing a native application even if it were available, or if I had a Mac or Windows. Web apps proved to be good enough for issue tracking (maybe I'm telling this to the wrong people given your choice, which I respect), my browser is open all the time and it has offline capabilities. Furthermore, it can be updated more conveniently.
Another point is that issues are useful if shared. I shared links to issues to customers and coworkers countless times and included them in reports. A web client solves at least one problem, maybe two. First, they might not want to install (or pay for) another tool. Second, Ship references issues with the ship:// url, which won't work unless you have Ship installed. A https:// url would work for everybody but then you need to share two different URLs which would be cumbersome. I'm sure you already found a solution to that.
Your site doesn't address explicitly one fundamental aspect: the data are hosted on your server, like issues stored in GitHub, Jira, etc and you're selling the service, or will be. Is this correct? What's the pricing? Thanks.
When I worked at Apple we used a native Mac issue tracker. It was much nicer than anything I've used before or since. I hate having to click-refresh-back-forward in a browser window, whereas a native client can have multiple windows, one for my assigned list, one for a search I did, then I minimize that search window and make a new window for a new search, then I cmd-H to hide the whole app without also hiding my browser.
At my current company we have an in-house project/issue tracker system which isn't quite as good as Apple's IMHO but very customized to this company's workflow. For my at-home consulting projects I try various web apps, most recently Mantis.
If you are planning on expanding to other platforms (iOS and Android, especially), maybe considering going with a C#/Xamarin-based project. It'll save you a lot of work by allowing you to re-use the underlying code for your app(s).
Which platform do you prefer?