I'm going to totally disagree with the accepted answer.
PGP/MIME is more secure than PGP/inline
PGP/inline is in fact considered less secure than PGP/MIME for a number of reasons:
PGP/Inline does not encrypt the complete message body but requires to protect each part of the email message separately which is why it cannot proof authenticity and integrity for the complete message. This causes several problems.
Encryption
With PGP/inline, emails may contain encrypted as well as unencrypted parts. Therefore, the recipient might get the impression that the message came encrypted while in fact only a part of it was indeed encrypted.
Signatures
Inline PGP signatures are prone to several other failure modes, up to and including undetectable message tampering. Because PGP/inline can sign only parts of an email, unsigned parts can be existing or being added, and the recipient might not be aware of it.
See Inline PGP signatures considered harmful for more details and an example.
Bottom line
Do not take my word for it. From the GnuPG FAQ:
Should I use PGP/MIME for my emails?
Almost certainly. In the past this was a controversial question, but recently there’s come to be a consensus: use PGP/MIME whenever possible. The reason for this is that it’s possible to armor email headers and metadata with PGP/MIME, but sending messages inline leaves this data exposed. As recent years have taught us, the metadata is often as sensitive as the contents of the message. PGP/MIME can protect metadata; inline can’t.
Other disadvantages
Not necessarily connected to security (though some are), but definitely even more reasons to go for PGP/MIME:
- PGP/Inline does not properly support non-ASCII texts, so HTML messages as well as messages containing umlauts or other special characters can create severe problems.
- PGP/inline cannot handle attachments.
- PGP/inline is an undocumented non-standard format, which causes compatibility issues, while PGP/MIME is well defined in RFC 3156 (MIME Security with OpenPGP).