It will depend on how you cook and size of your dishware. It is really best to take a load of your dishes to an appliance store and try it out. We have the double, but after meals with just two of us (about half our meals) will typically only use the top. For larger plates and skillets, you will need to get the Tall dishdrawer (same size as the top of our double). Our largest plates and skillets do not fit in the bottom. Our dishes, glassware, and silverware for two, a small-med pot and one or two small-med skillets and a small mixing bowl will easily fit in one Tall dishdrawer. Fitting more than one large pot or an extra large skillet can be done, but it is an inefficient use of space (skillets fit poorly in the tines, so angle in and limit space for plates; pots block water so you can't use the flip-out shelves above them). Sometimes we'll hand wash one skillet or large pot that wouldn't fit in the one with the rest of the stuff rather than start filling the bottom unit. If your cooking process uses multiple pots, multiple mixing bowls, a 2 or 4 cup measure, food process parts, etc, you will likely not be able to fit them all in one. It's the prepware that will get you; regular eating dishware loads small, that won't limit you. I do find the dishdrawers fussy about proper loading in order to get clean properly since the water is bottom up only.

I would not even try to cut in to the K&T or add to the circuit at all. A dishwasher should usually be on a separate 15 or 20 amp circuit, I would maybe think about putting it on with the disposer if you were aware not to use them together and they were on more modern wiring. Highly suggest that you leave the K&T alone since K&T is most dangerous when it has been modified incorrectly or overloaded. Instead go get some 12/2 romex cable and pull a new circuit to the new dishwasher from your breaker panel. If your home still is using a fuse box then you need to hold off on the dishwasher project and get a new breaker panel installed first. if your homes K&t wiring is ok and not damaged or unsafely modified your electrician can just put all the k&t circuits on 15 amp breakers if your local code allows k&t to be still in use. I am in an older home that still had some K&t when I bought it. now I have it down to only a few circuits and those are mostly just running lighting and ceiling fans that were in the house. I had to add circuits to the upper levels. I am adding a dishwasher my self very soon too and I will just put a new beaker in for it.

Regus_patoff is right. One of the biggest deal makers/breakers for me would be "how easy is it to get service?". The high line appliances cant be fixed by just any tech. Im going through the same thing right now with my Bosch washer. The only people who are qualified to work on the machine charge $100 just to knock on your door, thats includes NOTHING else! I opted to diagnose the problem myself. It took me approx 10+ hrs to figure it out, but I found the problem. Something to keep in mind for when your warranty is gone. TO answer your question about which one will clean out grease/oil stains better. You need to look at which one has the highest wash temps. High heat breaks down oil/grease. The temp boost cycle on Bosch hits 155 deg, it does a pretty darn good job of cutting the oil and grease on my work clothes. My uneducated guess in this situation is the LG w/steam would clean grease better.

You can NOT alter the existing K&T circuit to run a DW on it. If it can take the load, (questionable), then you could plug a DW into the existing outlet. But that's it. If you need to alter the circuit, you will have to run a whole brand new circuit from your electrical panel to run the DW. There are a LOT of insurance companies out there that won't even insure a home with K&T. And the main reason is that homeowners like to up their electrical demands on the wiring by hacking at it without replacing the K&T, which leads to fires. This is NOT a path you want to go down. Either leave the K&T completely alone, and that means no cramming in insulation around it or trying to use it to further extend or alter a circuit, or rip it all out and have the home completely rewired. If you are attempting to put a modern kitchen in this home, then the best approach is to rewire for that kitchen. Don't touch that K&T!