Acoustic/Electric differences  

My suggestion to you would be to use a really heavy gauge string. I've played both electric and acoustic; I always used ultra-light strings on my acoustic so I never developed the problem of using too much pressure. Hope the heavy strings help; that's all I can really think of.

i agree, a heavier string would make a difference.
or you could try an retrain yourself to not use as much pressure on the electric.

To me acoustic is the only thing I have been able to play. I have a couple of electrics and to me they just don't have the clear rich tones of an acoustic. I have the same problem the strings always sound out of whack to me

These guys have all good answers, and I just want to add, that when the strings get old, they have more trouble staying in tune also! The more you use them, the older they get because the acid in your hands wears them down!
When I was playing 6 nights a week, I had to change strings every week to keep them new!

To Me, playing an Electric guitar compared to playing an acoustic is is almost like playing a different instrument altogether. Electrics are so much more sensitive to the movements of the finger and stings. The pickups on an electric are designed to amplify every nuance of any movement.

I guess I was fortunate to begin playing with an electric, so going from that to an acoustic isn't nearly as noticeable in the difference of the sound being produced.

Another thing you might try is tightening up the strings. Granted, it is going to being putting the strings in a different key than your use to.