Which is better 410 stainless or 304 stainless steel for fastening screws that need to be electrically conductive and are under vibratory and side load stresses?

First of all, a stainless steel is a steel that has > 10.5% Chromium (Cr); this ensures development of a chrome-oxide that prevents further oxidation.

The 300 series of stainless steels differs from the 400 series in that the 300 series has both Cr and Nickel (Ni) - the 400 series has only Cr.

304 stainless steel has 18% Cr & 8% Ni.

316 stainless steel has 16% Cr, 10% Ni, & 2% Molybdenum (Mo). I believe this added Mo increases corrosion protection from chrloride-induced corrosion.