I have and use both budget sound cards (less than 50 bucks - posted an example below) and Fiio products (E17 + E09k), and I find that E17 provides:
a.) Slightly better sound production (mainly slightly better detail - but it could be that there is less noise)
b.) Blacker background (quieter) - I beleive this is because like wafflezz stated, its outside the computer. This gives me warm and fuzzies.
c.) More flexible in setup options (especially paired with E09K)
d.) Portable if I want it to be
The soundcards (again budget ones), I mainly use for convenience when I know I won't be hooking any other parts of my equipment up, and when I am not demanding the highest fidelity/flexibility out of the system. Or if it the computer won't mainly be used for headphones, but instead a speaker rig via a receiver. However, there is a certain beauty in simply plugging a pair of headphones straight into a headphone jack. But I always usually end up wanting to tinker, and when I tinker, many things that you buy tend to be external to the computer, and once you go external - you often defeat your soundcard via a seperate dac/amp combo... and then the options multiply quickly, and then you spend every waking moment on head-fi!
I would go with an external device so that you can have more options. However, if you think that you may simply be satisfied with an upgraded sound card - try that as well. In the end, only you can really decide what is "good enough" or to your liking.
Here is an example sound card that I use for reference. I also have 2 of the PCI versions of this card.
http://www.amazon.com/gp/product/B007TMZ1BK/ref=s9_simh_gw_p147_d0_i3?pf_rd_m=ATVPDKIKX0DER&pf_rd_s=desktop-1&pf_rd_r=1G8BEXE09B4FRNF13JN6&pf_rd_t=36701&pf_rd_p=1970559082&pf_rd_i=desktop