First of all , i don't prefer using master mixes because it seriously limits your capability of thinking out of the box. The mentioned troubleshooting guide in those kits don't let you go on altering Mg2+ which definitely has a role in stabilizing polymerase activity which is abrogated by sybr green I .
What i would insist is using sybr green or evagreen or LC green dyes with a homemade preparation of master mix.I am attaching a pic of melt peak and Ct of one of my amplification with home made master mix and Sybr green I.There was no extensive primer dimer formation as confirmed by Real time Peak. Worked better than AB Sybr green I qPCR master mix, in fact AB qPCR MM didn't amplify at all.
Now coming to the you question, theoretically Eva green dye is better than Sybr green, provided those master mix are amplifying you desired product.
Well I've only used Evagreen, and it worked fine for me. As I understood from the manual, it claimed that Evagreen is a modified Sybrgreen that has better intensity and efficiency.
Eva Green works better than Sybr green in terms of inhibition and fluorescence, however you can also use Syto 9 for the same purpose, it works quite similar than Eva Green.
I usually work with Sybr, but me too I have the doubt about what is better as I'm moving now on experiments that need to detect genes very poorly expressed.