Safer? I couldn't tell ya' though I guess it depends on what you are worried about.

As far as expediency goes you should use whatever format the provider prefers. A lot of girls don't check TER on a regular basis so using TER messaging to book or make initial contact with a lady may not be the best way to go.

Is there a consensus regarding whether it is safer to message through TER instead of Gmail or other common email providers?

In addition to what Boston said, what do you mean by safe?  The only safety you can exercise is anonymity.  But at best case scenario, if someone really wants to know where you have been, they can do so without even doing anything to your pc by intercepting the packets of info leaving your pc in which case neither medium would matter.  For your research, it's called packet sniffing and a quick google search will blow your mind.  I'm not sure how it works for smartphones, but whatever you do, make sure all your info attached to the acct is unique and when finished, be sure to clear your machine of browsing history, cookies, passwords, and the like.

Personally, I prefer contact through my email address (which is a Gmail account), because I'm simply more likely to actually see it! PMs tend to get kind of lost in the shuffle, and I definitely don't check my PMs daily like I do my email.

However, if you want to use your TER handle to add to your screening oomph (if you want me to also check out your White List or reviews, for example), it is nice to also send a quick note through the PM system to further establish that you do own that handle.

Not too long ago, providers and hobbyists used a couple of free encrypted email services:  Hushmail.com and safe-mail.net.  The email was encrypted if both sender & receiver had accounts.  I still have my SafeMail account and I wish others would use it as well.  You're not being 100% anonymous, but, at least you are making it harder.