one difference: Letsencrypt certificates are only 90 days valid, so you should use a client to automate the renew. Typical after 60 - 85 days. Check
If you buy a certificate, the validation is typical done by sending a mail to hostmaster@yourdomain (or one of some other special mail addresses) with a long link. And you have to upload a CSR manual. Then the public key + signature is sent back via mail, so you have to install the certificate manual.
The "Guarantee"? I've never understood that.
Letsencrypt only offers domain validated certificate, no OV or EV.
My personal position: Domain validated certificates are enough.
I've been looking, and have yet to see an instance where one of these "guarantees" actually paid anything--probably because the set of circumstances under which they would pay is so incredibly narrow. (edit: see also:
Other than the validity period already mentioned (which won't be an issue in a properly-setup installation, because the cert would renew automatically), Let's Encrypt doesn't issue EV certs. If you value those, you probably shouldn't (really), but if you still do, you'd need to use a different CA.