In my opinion,
The main difference between let's encrypt certificate & paid certificate is the lifetime (LE would always be 90 days and others have at least 1 year)
The other difference (that worth noticing) is the way to request the certificate.
Let's encrypt mainly support two verification methods : server based & DNS based, while other CAs support email based etc...
Not really... How do you obtained the certificate originally? You could renew the certificate via DNS challenges...