DRY code for sending email with SendGrid
Since the code that actually sends the email is the same and only the objects are different, then you can abstract out the sendgrid.send() into a function say sendEmail() that accepts an Object as a parameter since that's what the abstract code does, that's for readability.  In the callback function in sendgrid.send() ... you already have a return so anything after that doesn't get executed so don't need the else.

Declare the object for both alert and confirmation first. req.body is repeated in 3 places to declare that too.

Finally, invoke the function sendEmail with twice with each of the objects declared.

var body = req.body,
    alertObject = {
        to: "my@email.com",
        from: "myother@email.com",
        subject: "[ALERT] " + body.eventDate,
        html: "SOME HTML"
    },
    confirmationObject = {
        to: body.email,
        from: "my@email.com",
        subject: "[CONFIRM] register" + body.eventDate,
        html: "SOME HTML"
    };

function sendEmail (emailObject) {
    if (emailObject) {
        sendgrid.send(emailObject, function (err, json) {
            if (err) {
                return console.error(err);
            }
            next();
        });
    }
}

sendEmail(alertObject);
sendEmail(confirmationObject);