Normal attack damage is about 50% of damage output. I expect a 4% double attack rate increase to increase the average attack rate by a little less than 4%. So damage would increase by a little less than 2%. The effect on Burst damage depends on what your bottleneck for Full Bursts is and whether you're addressing it. 4% double attack on all characters would increase Burst accrual rate by a little less than 4%, buffing Burst damage proportionately.
Meanwhile, I reconsidered the effect of additional character attack, and additional character attack should increase damage by about 46% of the character attack value (2.6% for 6%) in a maxed team using 2x +45% elemental attack eidolons. Meanwhile, +500 attack will increase damage by about 1.3%.