Here is an FAQ that discusses some of the differences: https://ttlc.intuit.com/questions/2942039-what-s-the-difference-between-turbotax-online-and-the-turb...
I personally favor the download product because it allows me to look at and enter data directly onto forms. You can only see the form 1040 using the online product unless you pay for the product and then create a pdf. The download product also has a "what if" feature that allows you to play with different scenarios without affecting the tax return that you are preparing. For example, if you wanted to look at filing married filing separately vs. married filing joint, you can do that with the "what if" feature in the download. It is not available with the online product.
Just be sure you password protect and back up everything in case your computer is damaged, lost or stolen.
With download, you can make a copy of your return and then manipulate it all year as a preliminary return for the next year.
Online is usually cheaper, but this advantage is wiped out if you have to upgrade. You can do all types of returns in the lower download versions.; e.g. you can do a self employed schedule C in Deluxe.
An older computer may not have the capacity to handle a download.