It's best practice to send both. Some recipient mail clients will default to the text version only, so you should always include both.
Sanford Whiteman provides a great explanation here: html only?
If someone is using a mail client that supports HTML, they almost always download the HTML markup if it's present. It's the embedded assets in the HTML (i.e. IMGs) that, in clients like Outlook, are not downloaded unless the lead chooses to do so.
Rarely is the lead shown the true Text version first without having made that deliberate choice, and you should definitely accommodate their preferences. Sometimes, the mail client supports "Text First" or "Prefer Text" as an option and someone chooses to view the Text only versions of all emails, even when the client would be capable of showing them the HTML version without images. (I have my primary mail app set to Text First for a selection of senders.)
In the end, there are only disadvantages to sending HTML-only emails. You would only alienate those who use non-HTML mail readers or have a Text First type of switch turned on. The exception may be when you have a preference center that allows for Text Only to be selected, and you don't want to maintain a working Text version on the HTML side. In that case you can just leave a single line in the Text section that says, "We do understand that some people prefer text-only emails! Just go to http://example.com/prefs/textonly and we will send you a text version from now on."
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