Both of them offer you a lot of options in terms of design and features. You may eventually outgrow them, but I will describe ways you can upgrade, and when you should.
What is a WordPress.com Website Good For?
It’s great for a personal website or blog. People who have other websites sometimes create a free website to be a sort of feeder to their main site.
What is it NOT good for?
WordPress.com is not meant for commercial use, according to their terms of service. People do push the envelope on this, quite a lot, and every now and then a site someone has built on WordPress.com suddenly disappears.
This happened recently to a site that a friend of ours and my husband had been working on for years: one day they went to earthbagbuilding.wordpress.com and it wasn’t there. Kelly emailed wordpress.com and within a few hours — long hours to us! — he received an apologetic email. Evidently some automatic process had declared that the site was spam and it had been taken down abruptly. However, the person who emailed said the site had been put back up. We decided the time was ripe to move… I’ve told the rest of the story on the site that we moved to, the way we moved from WordPress.com to a self-hosted site. Self-hosted simply means you pay for webhosting someplace.
So now that that site is moved, we are making some steady money from it, both through ads and through selling our products. It was actually a move that was long overdue!
What about Weebly?
Weebly.com hosts literally millions of websites, many of them using its excellent website maker software for free. My husband recently set one up there, and soon discovered that the group he is a part of needed some specific features, like the ability to have some pages private. So they upgraded for a few dollars a month. You can see their site at cbvillage.net, just as an example of a Weebly site.
So.. if think you’d like to make a free website, this should be enough to get you started!