First thing I'd look at is simply this: "Would the stand hold the empty tank if you removed all glue and nails/screws and fasteners?"
Glue and screws should only hold the wood together, all structual support should be from the wood itself. If fasteners are holding up the weight thats a bad thing. It should be the wood holding up the tank, and fasteners just to make sure the structure doesn't fall apart.
Often when stress testing something designed to hold weight you would submit the structure to double the weight/stress it would have under normal conditions. If it can hold double the weight without showing signs of distress then it should be good. This method is used for safety ropes, cables, SCUBA tanks, etc. Considering the impact of the stand collapsing I would use the same technique.
Just make sure you inspect the stand well to make sure the extra weight doesn't cause some unseen damage.
A quick easy way to stress test, get a couple friends to stand on top with you, just make sure you won't hurt yourself if the thing collapses.
Now for your pictures specifically, the first counter looks flimsy, made of particle board, without proper support on the bottom. Just from what I can see I'd guess it would be a bad choice.
The dresser looks solid. The framing inside for the drawers add extra strength. I'd want to see it without the drawers but from the outside I think it looks good. If it was a choice between those two, i don't think I'd even try kitchen counter.
