Please see my previous post about my Closet Laundry. This is on the first floor, but above a basement, on a hardwood floor. The vibration is minimal, IMO. Asko has a suspension system that controls vibration. I will say that there is "jet engine" noise from the high-speed spin of the washer, and a low rumble from the dryer. I suspect that you'd get this from any similar machines.

I have the compact Askos stacked on the second floor of a 100 year old house. They are in a corner directly on the maple hardwood floor. I, too, agonized over the possibility of too much shaking/spin before I purchased them last summer, but there's been absolutely no problem in this regard. They are very stable, noise is minimal, and I started the good habit of turning off the water supply after each use to minimize the possibility of leakage (I did not install a drain pan). So far, so good--it was an excellent choice.

"this is on the first floor, but above a basement, on a hardwood floor."
"I have the compact Askos stacked on the second floor of a 100 year old house. They are in a corner directly on the maple hardwood floor."

In my opinion it doesn't have much to do with the surface flooring you are mentioning (other than tile over joists is likely to crack).

It has to do with structural flooring below. Variables like spacing and especially thickness and length of joists make a big difference, and even what the joists reset on (eg along beam which can add bounce vs a masonry wall). The other major factor is whether you are placing the washer near the end of the joists or where joists sit above a bearing wall. as you go out toward the middle of a joist it is going to resonate (bounce much more).

What is most important about surface flooring, hardowwwd, or vinyl or composite over plywood is how securely it is attached to the joists

It isn't correct that Samsung is the only maker to address this. There are a variety of schemes both in the internal suspension and vibration compensation mechanics by many makers. There is also programming for how less than optimal balance situation will be dealt with (repeated attempts to balance, slower spins and or slower spin gradually increasing in speed.

It is salesman's "spin" (sorry for the pun) that says only samsung has dealt with this. Consumer reports, while imperfect, started last year to do accelerometer tests. It is very clear there are many make/models which are pretty bad and quite a few which did pretty good. The samsung they tested scored the same as the whirlpool duet on vibration.

Also of key importance if you are going for a second floor install is return policy of your retailer! My locate sears is telling me they will give me a 30 day no questions asked return so I can get a top loader if their is a problem

I had my Asko pair on the second floor of my townhouse for three years and never once had a problem. Once you level the machine, the independent suspension inside the Asko will reduce vibration by 90%. Asko used to do this ad where the machine was spinning with a wine of glass on the corner edge. Of course the entire cycle was done and the wine didn't move a hair or show any swishing inside the glass from the vibration.

I think Asko has one of the best suspensions out there. Great at minimizing vibrations by physically isolating the drum using pneumatic shock absorbers attached to the washer body. One time I left a glass of wine on my machine just like in the ad! I always have a glass of wine with a little classical music as I settle in for an evening of laundry... and after about 20 minutes I remembered what I had done and raced back to the laundry room. To my surprise, the glass was sitting right there, still as I left it, while the laundry was spinning at 1,600 rpm. Amazing.

It isn't correct that Samsung is the only maker to address this.

I know that Maytag Bravos (HE toploader) gets high marks for virtually no vibration. I've read a number of glowing reviews from owners whose Bravos washers are on a second floor.

My Bravos is not on an upper floor, but vibration is definitely very minimal -- even on the highest spin speed. (I would say it's nonexistent, which is as it seems to me, but I can't prove that statement.)