You may want to download your imessages for various reasons. PDF is the most popular and standard file format to present rich content documents, including well formatted text and images. So PDF is really suitable for storing iMessages from your iPhone.
The advantage of PDF file is maintaining the native style as of Messages.app, including photo attachments. With iBackup Viewer, you can easily export iMessages to PDF files from iPhone backups.
Here is a step by step tutorial to save iMessages to PDF:
Launch iBackup Viewer after installation.
Open the backup by clicking the backup icon.
Click on "Messages" icon to open messages
Enable options to Save photos in PDF in Preferences
Save iMessage to PDF
Options for output PDF
Advanced options for messages output
Click "Save" and choose a folder to finish creating iMessage PDF file.