They do not supposedly have the same sensor. Go to DXOMark, click the grey "Compare up to 3 items" button, and you will see that there is a bit of difference.
E.g. click on "Measurements", "ISO Sensitivity". Those are measurements against the standard ISO sensitivities.
More importantly "SNR 18%" shows that the 600D is a little bit less noisy than the 100D except at ISO 100.
Dynamic range: 600D is the winner, color sensitivity: at low ISO, there is a match, but higher ISO, the 100D is winning.
The differences are not big though. For me dynamic range and color depth is important, and also noise performance, so I would go with the 600D. Others consider different parameters. These cameras are pretty close. Even the DXOMark scores line up pretty well.
However, I do think they are different sensors.
UPDATE: And just read that the sensor size is a bit different, so I am right :-) (5208 x 3476 vs. 5344 x 3516).