With a dedicated app, you go into the store and install it and then you have it in your apps that you then can place everywhere.
With a website, you need to have the browser, navigate to that website each time. And yes, you could put a link to that website on your home screen as well but not many user are probably aware of that being an option.
I know that but I still would prefer a dedicated app because it is easier to manage and use more features of my phone. For example, I just tried it on my android phone and the link to a website always opened a new tab in my Firefox.
Then I can manage the notifications of that app depending on what I want it to notify me about.
I can’t do that specifically for a single app or website in a browser.
On the other hand, I also wouldn’t want to miss a website because I am not always on my phone and, in some cases, it is way more annoying to do something over the phone because I am just not used to it (like writing this comment). Doing that over a website version that I can access on my PC is much easier and convenient.