The most common question, and the answer is less dramatic than vendors suggest.
WHAT IS IDENTICAL
The encryption. Free and paid certificates use the same algorithms and key strengths. The padlock. Visitors see the same indicator. Browser trust. Both work everywhere. Search ranking. No difference.
WHAT DIFFERS
Validation level. Free certificates are domain validated. Paid ones can be organisation or extended validated, though browsers no longer display the difference prominently. Warranty. Paid certificates often carry a financial warranty, which is almost never claimed. Lifetime and renewal. Free certificates renew automatically. Paid ones are typically annual and renewed by hand, which means they can be forgotten and expire.
THE PRACTICAL POSITION
For virtually every business website, blog and shop, free AutoSSL is the correct choice. It is automatic, it does not expire unnoticed, and it costs nothing.
WHEN TO PAY
When a partner, regulator or payment processor specifically requires a validation level the free option does not provide. Ask them to confirm the requirement in writing before spending.