Onboard D/A for WAV, MP3, Movies, etc are generally good enough if the noise level is low enough. The biggest difference is in the on board synth. Playing games uses MIDI and the sound card produces the sounds. There are 2 versions. Hardware and software.
Hardware had an on board synth. It can be as simple as an 8 bit video game or as complex as full wavetable sampled sounds. An onboard hardware synth will sound the same on Linux or Windows. If the wavetable synth is XG compatible or similar, the sound is great. If a cheap synth is used it will sound like a casio entry level keyboard or 8 bit videogame.
Some cards use soft synth's with soundfonts. These can be very good sounding with inexpensive hardware as the synth runs in the OS and just sends the bitstream to the card for repoduction. This uses some system resources and requires installing the proper driver to include the synth and soundfont. This can mean great game sound in WIndows, but no sound or missing sound in Linux for games, unless you load a soft synth on Linux, install a soundfont, and enable it through Jack. While the combo does sound great, it is a resource drain.
Now, which is better? Mixed bag here. Some on board sound come in either variety. Same with add on boards.