How can a voltage follower op amp amplify?
I would suggest that you place a load resistor, perhaps 2K along with a parallel capacitor of 100 pf on each of the outputs to ground.  You are slewing the positive input faster than the output (and hence the negative input) can keep up with, which results in voltage difference on the op amp inputs.  This type of op amp's push-pull output will behave better if you give it some load. Your breadboard probably had an (inadvertent) low-pass filter on the op amp positive input.

It's a little counter-intuitive, but you need high speed op-amps to provide adequate feedback to reduce higher-frequency open-loop amplification.  Loading the output will help some, but I think you will still have a little overshoot on the output, although certainly not 100%.