This isn't a situation you're going to run into, but let's run with it. All else being equal with a given set of bikes, visually you could probably just barely tell that one bike had a higher or lower BB than the next. You'd probably need a tape measure. In general, your bike with lower bb is going to transition from turn to turn ever so slightly faster, probably an amount unperceivable to most. It's also going to have pedal strikes more often. The bike with the taller bb height is going to be just the opposite in both respects. Keep in mind that without rider weight, bb height is deceptive on any bike with suspension. Its worse with full suspension vs hardtails. Proper suspension sag is typically taken into account in geometry specs, but on the showroom floor suspension bikes will have exaggerated bb heights.
Now let's talk real world.
We're really only talking about a few cm of difference in bb height even in extreme case comparisons. For instance, looking at Trek's xc race hardtails and comparing them to their downhill bikes, you've got less than 6cm of bb height difference. That's not insignificant, but we're basically comparing apples to oranges at that point and looking at 2.5 inches of difference. Amongst a given category of bikes you're going to have very little variance- probably less than a centimeter.
It's important to keep in mind that bb height is just a small piece of the puzzle in terms of handling dynamics for a bike. There are other factors of frame geometry that I would take into consideration first, such as effective top tube length (the bike needs to fit) headtube angle (how quick will the bike initiate a turn) and wheelbase (how quick will the back of the bike follow the front of the bike). When those are equal I would start considering chainstay length, headtube length, and bottom bracket height. Those are all pretty much in order.