The short answer is no. There are no significant advantages to either. With the advances in internet speeds and 5G entering the market, downloading software is close to becoming obsolete. Still, players with slow internet speeds may want to consider this option because the loading times will be quicker and the data usage less.
The benefits of playing in a browser are that you can log onto the internet at any time without issues. The other is that you can access several providers simultaneously, which is not available with downloadable software.