I can only speak for the LG Wafeforce.
I would opt for the LG if it were me, they seem to be very well made and I have not any problems with mine at all.

I have heard people having issues with repair/service work but name one brand where you don't see the same issues?
I think it is largely the fault of who is in your particular area as far as repairman problems.

I have no idea how we would fare if something happened to ours and I hope I never find out, odds are pretty good I never will as so far in 40 years of doing laundry I have yet to ever need a repairman to come out.

All I know is ours works great, I can add extra if I feel the need though so far never have.
It has an internal heater that works with 2 cycles, Bright Whites (122degrees) and Sanitary (158degrees)

What model elite and wave force are you looking at? The 5101 wave force has a heater the other does not. Too many models of the elite to list with out more info. My brother and sister inlaw got the 5101 wave force just after Christmas and have not been thrilled with it. They have had problems with it going out of balance on spins, they had a tech out last week and were told to spin at lower speeds. That doesn't help as it starts to shake even at low speeds. I've not seen it try and correct the load on it's own as it's suppose to do. I have seen it walk because it out of balance at which point he paused it moved two or three item and then it was fine. He was surprised to see the the brackets that hold the suspension rod and all the weight of the tub and laundry are made of plastic, not metal like most top loaders.

oops ,I meant to include that it's the LG waveforce 5101hw and the kenmore elite29272

They are both LG, but I see nothing that would indicate a heater on the kenmore unit.