There are two parts to the question here: better quality, and different exposure.
The better quality answer is simple: yes, there are significant differences. Cameras with larger sensors have an inherent advantage, but technology is advancing so quickly that it's often the case that technology generation is more important. Within sensors of the same size, it's definitely the case that different technology gives an edge in noise.
The other question is a bit harder, because while in basic theory it's the same, the standards for what exactly constitutes correct exposure are subjective. And, I mean that literally: the actual standards allow some latitude, and so you'll find that the brightness of the result given by the same combination of shutter speed, aperture, and ISO varies from brand to brand. (Maybe from camera to camera, as in your Nikon-to-Nikon example, but more tellingly between companies.) Dpreview used to measure this and provide a comparison to their own standard in their reviews. For example, this chart indicates that certain cameras from Pentax and Nikon match their ideal, where the Canon model was actually using a higher nominal value.
But, they don't do this anymore, probably because it's easily misinterpreted as a value-judgment about quality (or even honesty!) when it's really not. The same camera in that review often generated review complaints about a "tendency to underexpose": some people didn't like like that the chosen brightness was what DPreview calls exactly accurate in their chart.
But, having gone into some technical detail here, it's important to stress that these differences are very small, measured at less than a stop. Modern sensors have dynamic range such that this is unlikely to matter at all if you want to adjust the result slightly in post-processing. (Or, if you know that your camera tends to meter more darkly or more brightly than you like, remember that and dial in EV compensation.) In any case, unlike with ISO noise, it is not an indicator of "better pictures.