For example, if this spark gap has a kilovolt of power behind it @ 1A and the other is also at a kilovolt but is @2A will there be a visual difference (i.e. will the one with higher current be thicker, have a different color, etc.)?
Yes there is. I ran across an automotive site which did such an experiment where they varied spark amperage, while maintaining a constant gap.
In the article, "Understanding, Testing and Calibration of Ignition Coil Dwell Time", the authors used a 5mm spark gap, while documenting the appearance and oscilliscope waveform of a 2 amp spark and a 7 amp spark (qualifiers- inductive ignition, free air test gap):
2 Amps of coil primary current
7 Amps of coil primary current
In the waveforms they recorded, the 2 amp spark lasted 0.5 milliseconds, while the 7 amp spark lasted 1.4 milliseconds.
There may be color differences as well, but I haven't been able to find concrete documentation of this, beyond a little orange in the center of the 7 amp spark above.
I spoke with the author of the above article in an e-mail exchange, and he said ( among other things ):
Spark colour in a given gap would mainly be a function of spark current and temperature.