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You've just described once of the differences between my left and right eyes - a significant diopter difference.
With two identical telescopes and two identical eyepieces I can confirm - from personal experience - you will perceive the image from each eye to be different.
This is because:
a) one eye has a different focal length to the other, hence the diopter difference;
b) to achieve focus one eyepiece or the other will be moved in or out relative to the other to compensate for the diopter difference in your eyes, and
c) the resulting overall combination has a different angular magnification one eye compared to the other.
Whether you're brain can fuse the images is another matter - you might be able to; I never could despite three operations under the age of 3.
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