Friction is too complex to make generalities.
There are different measures of surface roughness. Some irregularities lock together, others reduce the interaction. Solids have different elastic constants, slippage may wear off irregularities, interatomic bonding may occur at contact points, friction is affected by surface films -- oxides, adsorbed moisture (graphite is a poor lubricant in high vacuum where it loses its moisture content), etc., etc.
Are your solid surfaces more like step function, rolling hills, sawtooth, etc. and are both the same?