track bikes are stiffer and the forks often have no rack the frames have fork ends and high bb's different geometry and twitchy handling alot of them are drilled for brakes but will not work well with brakes as the currnet trend is to ride a track bike on the street
as afar as 1/8 vs 3/32 3/32 is quieter and a little weaker the 1/8 has a little better mechanical engagement and is a little stronger the size of the chain doesn't matter both standards are track legal in the us
now if you are some idiot who will never ride in japan but has to have a keirin njs certified rig then be that way but 1/8 and 3/32 make no real difference except maybe you will find chains easier for 3/32