Webmail gives you acecss to your email via a web page displayed on your browser. The emails are stored on our server not on your local computer.
Which is best? That depends upon how you use the internet. Webmail is available to you anywhere you go, while to run an email client (Outlook, Thunderbird etx) you must be at the computer the program is installed on.
We use a combination of both for our own business. Thunderbird catalogs customer and vendor information, emails, to do tasks etc. And when we are on the road, Webmail gives us instant access to new emails. Sweet!