You can do pretty much anything from either one if you try hard enough.
But some things are easier to do with one than the other.
For instance, HTML is great for creating snappy looking UI designs. Of
course you can create great looking WinForms apps also, but it would likely
take you more effort.
Winforms tend to have richer functionality close at hand. For instance you
can keep a constant connection alive between your users and your database
(or other application components.) ASP.NET is stateless and that can make
passing data around more challenging.
WebForms require only a basic web browser on the client's machine, which
eases deployment and future upgrades. (WinForms require your application
and .NET framework to be installed on each user's computer.)
With WinForms you can have your entire app on one machine if you so choose,
with no network connection needed (depending on the nature of your app of
course.)
The look and behavior of your WebForm apps can vary depending on the web
browser(s) your clients are using. WinForm apps are not usually dependent
on web browsers to they tend to behave more consistently.
WinForm apps can interact with the user's computer more deeply. WebForm
apps have security limitations that prevent them (by default) from accessing
the user's registry, modifying files on their hard drive, and other such low
level tasks.
