Express is a more complete application framework.
Koa concentrates on core middleware functionality. The core Koa module is only about 2K lines of code.
Express comes with a complete suite of middleware features built in. Koa does have options for these features, but they are separate modules. You only have to include the modules you need.
Koa was designed explicitly to take advantage of the async/await keywords. You write more readable async code with Koa.