We just completed our kitchen renovation yesterday, and we replaced the old electric stove with an LG induction range from Costco when it was on sale in Oct. Costco doubles the manufacturer warranty, and the Costco Citi card doubles that, for a total of a 4-year warranty. We used it for two weeks before the renovation started and finally got to use it again last night.
During the renovation, we used a portable induction burner, and it cycled, as mentioned, and couldn't hold a steady temperature. The stove is much, much better, and I can leave a covered pan on simmer, and it simmers perfectly.
The portable burner squeals/shrieks/hums audibly, but the stove doesn't. Though, the stove has a vent fan that runs when the burners are on, so maybe that masks some of the sound? I don't know.
The bummer about LG is the access to parts. We have two companies in town that service LG, so with the extra warranty years, I'm willing to risk it. We have other LG appliances in our house that are 10 years old that - knock on wood - haven't needed any service calls, so I'm hoping our luck continues.
I agree that the quality of the pots makes a difference on the evenness of cooking. Our wedding present to ourselves - in anticipation of the kitchen renovation - was a set of AllClad induction-compatible pots, and they cook much more evenly than the hand-me-downs we had before.