I'll be looking for more input, but I like the second option better assuming that you place the tank astride the area supported by a 4x4 on either side of the tank. The concrete pillars under the 4x4 give them a lot of resistance to collapse.
I assume that you mean that the 4x4 and the 2x8/10 are all directly below the floorboards....no gaps.
1) Is there a pillar under the 4x4 at the load bearing wall? Or is that something like an I-beam and the 4x4 rests on it?
2) I assume the 2x8s are set between the 4x4 with no cuts, i.e., the 4x4 is apparently solid across it's length.
3) are the floor boads above the crawlspace perpendicular to the 2x8s? I'm thinking they almost have to be unless there is something else above the 2x8s.
4) where are the concrete pillars located? My basement had I-beams stretching the width of the house. I'm assuming you either have an I-beam somewhere, or several concrete pillars under each 4x4, possibly just 4-8 feet apart. 4x4s alone would not seem like enough to span the support for a house.
I don't think I like the first option:
1) the tank looks like it would basically be supported by 2x8s or 2x10s set 16" apart. If the 2x8s are simply under the floor boards and between the 4x4s, they are being held by nails/screws with nothing underneath. That would seem fine for a 5 foot span 16" on center for a basic floor. 2x8s should keep the floor solid and supported for 'normal' use. I'm guessing the areas under the kitchen and bathtub have a lot more support than that.
2) running parallel to the floorboards (see item 3 above) is good, but with most of the tank sitting in the middle of the 2x8s, I'm concerned you'll get deflection and warping to the floor. I'd want an engineer to tell me that I could to that safety.
3) in short most of the resistance to the tank in option one are the nails/screws for the 2x8's. As long as they hold, the 2x8's need to keep the floor from deflecting.
I have a lot more belief that the 4x4s sitting on top of concrete pillars (and if so an I-beam) would handle the load. In that case, you are relying upon compression.
However....I'm not an engineer (or even an architect or a builder.) Hopefully this will be corrected by someone who knows.
Many people (me included) will suggest that you have an actual engineer look at the crawl space and advise you. It will cost you some money, but it will probably be well worth it for peace of mind if nothing else.
a) there could be cuts made for wiring that may reduce the load rating
b) the supports may have been added with inadequate or substandard nails/screws
c) there could be aging, rot or damage that only an engineer or architect might see