A headphone amplifier CAN be an improvement depending on several factors.
Most integrated amplifiers have a headphone output that is simply taken from the speaker outputs and padded down with resistors. As a result of this the output impedance can be pretty high, when using a low impedance set of cans you can get some pretty severe deviations in the frequency repsonse.
A lot of integrated amplifiers also develop a little bit of hum and/or hiss as they age, with speakers you'll probably only pick this up when you put your ear next to the tweeter, but with headphones it can quickly become annoying, particularly with low impedance, high sensitivity headphones.
Some headphone amplifiers also produce noise, the Musical fidelity tube models are known for this. (Not really an issue on any but the most sensitive cans)
Both the Pro-ject (I have the Head Box SE II in my bedroom) and the Musical Fidelity are op-amp based models , with low output impedance and great specs and are dead quiet.
The Pro-ject I own sounds great, and effortlessly powers the most demanding headphones (Hifiman HE-6), it is built quite well, exept for the cheap volume pot and lack of an on/off switch.
If you are using Sennheiser models for home use (HD600/650/800 etc)or high impedance Beyerdynamics there's probably very little reason to buy a headphone amplifier (Although I owned several integrated amplifiers that had audible hiss even with the HD800), but when using something like Denon AH-D2000/7000, Beyerdynamic's low impedance models or headphones designed for portable use, chances are a dedicated headphone amp could make a difference. I don't know the impedance of your Audio Technica but suspect it is somewhere around 50ohm, which is very low for your integrated's headphone output.
Finally there's a little practical advantage to me: My amplifier is about 3m from my seat, and having a headphone chord running right through my room, with other people/pets walking around is a bad idea: A 5m interconnect and a small table puts my Headphone amp right next to my seat, with the added benefit of having the volume control within reach.