You're assuming that more pixels automatically mean better image quality. Sometimes what you get when you zoom in to view the results obtained with a higher resolution sensor (more pixels) is the ability to more clearly see the imperfections of your lenses as well as the imperfections of your shooting technique, ability to accurately focus, etc.

When you crop the 24MP sensor to view only the 10MP in the center you are effectively magnifying the image projected by the lens by a linear factor of about 1.5X.¹ But you are not increasing the optical resolution of your lens by the same linear factor of 1.5X, the optical resolution of the lens remains the same. That means the limits of the lens' resolution are now 1.5X larger than they were when viewing the same image at the same size.

If your lens can still outresolve your sensor, then it is not an issue. But if your sensor can outresolve your lens, you'll definitely see the difference, and the difference will not be in the direction you desire.

It's not just resolution, either. It's also things such as chromatic aberration, coma, astigmatism, geometric distortion, etc. You're effectively magnifying all of them by a factor of 1.5X.

Normally we would say you'll also be magnifying the image noise by a factor of 1.5X. But in this case, the 2014 Sony A6000 is of a sufficiently more advanced technology generation of sensor design than the 2006 Canon EOS Rebel XTi that the only way to compare the two in respect to noise would probably be to measure each under the conditions of your question and compare them.

¹ If the two sensors were the exact same size, the magnification factor would be 1.55X. But the Sony APS-C sensor is 23.5x15.6mm, while the Canon Rebel XTi APS-C sensor measures 22.2x14.8mm. That means the A6000 sensor is about 5.6% larger in linear terms than the XTi. When this is factored in, the difference in pixel pitch between the two is approximately 1.46X