The advantage of the professional vs. the free account is the number of options available to you when you create a tracking link.  If you have a free account, here’s what you get when you want to create a link:

There’s a spot to put the URL you want to link to, some notes so you remember what it’s for, and a description that’s publicly available to the audience.  Links created with a free account expire after 30 days by default.

If you have a professional account, you see:

Which gives you the same URL, notes and description fields, plus:

• The ability to add a title to your link both for organization and if you want to make a vanity link.
• Ability to add an alert email so you get notifications for each of your click-throughs.
• Password protection in case you want to define a password to access the link.
• Ability to turn the link on and off whenever you want.
• Field to set your own expiration date (if you have a limited time offer for example), or no expiration date at all.

Here’s an itemized list of what you get with the paid accounts.