I think your sim will learn cooking at the normal rate, but because the repetichopper will speed up the overall preparation, your sim may learn cooking slower than using the counter.
I've heard that the chopper increases the quality of the meals, but I've never tested it.
Both of you are correct. You produce better quality meals faster, but the reduced time also means less cooking skill gain. However, the extra skill gain from not using the chopper isn't really huge: when using that stove, the preparation part of the cooking process is the slower rate of skill gain. So theoretically, if you were grinding cooking skill, you'd max it faster by using the chopper because the portion of training that gives the least returns would be minimized. That gives you more time to actually use the stove.
Edit: "Grinding" in the sense I used it is an MMORPG term used to describe the process of training a skill non-stop with no other goal in mind than to increase the level of that skill. Anything produced from the process is typically considered waste and is disposed of in some convenient way (selling in bulk to other players, selling to an NPC merchant, or simply destroying it).
