Mixing for playback vs live shows

[yul]

I am very confused when it comes to mixing my tracks. I need to be able to play live shows and want to reuse some of the backing tracks from my mixes.

It seems that mixes deemed for home listening should be made to transpose between all forms of speakers/headphones and are generally bright to meet todays expectations

I don't use eq and usually balance my mix and synth sounds at the source to match the required spectra.

What happens of this should be played back on a full range PA I believe that my original mix may not be as effective since it wasn't built for live.

I really dislike eq'ing and wonder how other live shows manage this. Since my synths are patched at the source to sound open and shine, I can't imagine having to modify my sounds at the source just to add more bass for example.