I'm a TA, I deal mostly with corporate clients that just book airfare and not packages. But for what it's worth...
When I have clients tell me that they found for less online, I usually find that the sites they are checking don't add in all taxes and fees. Once the client discovers the real price, it turns out it's the same as what I found, but I give better customer service (not that the online places are bad, my agency just goes abover and beyond, that's all).
So, with that said, be very sure that the package your TA is offereing is exactly what is being offered online, right down to taxes and
trip insurance, otherwise it's not a true comparison. If everything is identicle (dates, flight times, hotel, insurance, taxes, extra things like tours/shore excursions, and any and all other extras) and you're still getting a better deal online,
let the agent know that you got a better deal online, but that you appreciate their help and will keep them in mind for your next trip. A good TA will understand why you aren't booking with them and that you at least gave them a chance to compete for your business. Because the next time, the TA may have the better deal but may not be as willing to help you if they think you're just going to use them to do all your research just so you can take your business elsewhere, you know?