To begin with, I'll address my personal experiences with and opinions on noise, insulation, price, and guarantors.
In my building, the walls weren't thick enough to block out very noisy neighbors, but neither were they paper thin. I could have a friend over and talk in a normal voice or Skype home and not appear to bother other people in the building. However, I did have a neighbor who came home at 1 or 2 am rather frequently and was either on the phone or bringing a boyfriend in tow. Against the otherwise completely silent backdrop of rural Japan, I could hear their vocal rumblings through my walls well enough to be woken up a few times, although never clearly enough to understand any words being said.
The tiny "1K" (that means: bedroom + kitchen-in-the-entryway) Leopalace setup, which is the most common type--although I've also seen 3-room family setups, is pretty good in terms of insulation. The door to the outside world is usually made of metal, which lets in all the cold during wintertime, but between that door and your bedroom should be another wooden door. When that bedroom door is closed, you'll have a nice, cozy living space. Running a computer and just sitting emanating heat from your body is enough to carry these tiny rooms through cooler months, and in anything more extreme than that, turning on the heater or air conditioner brings about almost immediate results.
I was able to get used to living in my place easily, and I think that's the most important quality of an apartment. However, I've gotta say that the pricing on Leopalace apartments is steep. The building I stayed in was new and in exceptionally good condition, but even so, other 1K apartments in my backwoods area were running for 10,000 to 20,000 less per month. Of course apartments rented on a monthly-basis (instead of with annual contracts) are generally a bit more pricey, but I think another part of Leopalace's pricing rationale is that you're paying for the amenities inside the room--rented furniture, appliances, and a provided Internet connection.
A big draw of Leopalace for foreign tenants is that they do not, in principle, require you to have a traditional Japanese-style guarantor to move into one of their facilities. In my case, the apartment had been arranged through work. However, later, when I wanted to arrange for my own private parking space, it was easy for me to walk in to the local Leopalace agency and sign up for one without a guarantor present. (They did ask for me to provide contact information for my closest relative in my home country, however.) And don't think that's because it was "just a parking space." It's true of apartments as well. (I sure as hell needed a traditional Japanese-style guarantor to get my next parking space, by the way.)
Over the next couple of weeks, we'll continue this series with detailed articles on furnishings and Internet connections in Leopalace apartments. Be sure to check them out. We as always welcome comments, and particularly would like to hear from readers who have experience living in Leopalaces. What is/was it like? Is the description here accurate? Any DIY tips on how to make the most of the cookie-cutter floorplans?