If the question is simply "will an audio interface do better as a headphone amplifier?", then the answer is "probably not".
A dedicated headphone amp will usually be superior to the headphone amps built in to most audio interfaces. Although higher-end interfaces typically have decent headphone amplifiers, the entry-level products you're likely considering do not. At least, I've yet to hear one in the < $1,000 price range that compares to a good standalone headphone amp.
Although Cactus' advice about external interfaces is totally legit, not everybody actually
needs one. If you're working solo (no need for multiple headphones and headphone mixes) and doing 100% ITB productions (instrumentals using only soft synths and/or samplers), then you might just get away with using the integrated audio interface in your laptop.
However, if you plan on using a microphone for
anything, then the integrated audio interface in your laptop will not be satisfactory. If two or more people need to monitor simultaneously, the integrated audio will not be satisfactory. If you want to switch between multiple speakers/headphones, the integrated audio won't be satisfactory. So whether you
need an external interface or not depends on what kind of music you're producing, what instruments you employ, whether you collaborate with other musicians, and if you'll always be using one pair of headphones for all monitoring.
Eventually you're going to want to hear your projects through reliable speakers rather than just headphones. You'll find that music mixed and mastered on any headphones are going to be hit-and-miss as far as how they ultimately sound on other peoples' speakers and headphones. Quality speakers for monitoring will remove some of that uncertainty and improve consistency. At that point you're going to want a good audio interface.
Whether or not you buy an interface, those Senns
will benefit from a headphone amp. You'll be able to play them much more loudly before distortion sets in, and the frequency response will be flatter. You've spent good money on nice headphones so it'd be a shame to go cheap on amplification.