Some basic numbers are good place to start answering this sort of question: you can measure the relevant material properties of various woods and see how close they come to the 'standard'; European spruce. As Michael says, with only limited horsepower in the strings we need to keep the top light if we're going to get any power or treble response. Reasonably low 'damping' should help too: we don't want the string energy being dissipated by friction or other losses in the wood. Strength is far less of a consideration than is often assumed; any wooden top of more or less traditional construction that is stiff enough will in all likelihood be stronger than it needs to be. Also, apparently cross grain stiffness is not nearly as important as it's often thought to be; it seems to have some acoustic effects, but is not as useful structurally. So, we're probably most interested in how stiff a piece will be along the grain, and how much it will weigh when it's 'stiff enough' for a guitar top.
If you're talking about pieces of wood of the same thickness the material property that determines how stiff they are is the 'Young's Modulus', abbreviated as 'E'. The E stands for 'extension': Young's modulus is a measure of how much force it takes to stretch (or compress) a piece of material of a certain size by a given amount. When you bend a piece of wood you're stretching the fibers on the outside of the bend and compressing the ones on the inside, so the Young's modulus comes into play; for a given thickness of piece the higher the E value, the harder it is to bend.
If you think about it, it's the fibers on the top and bottom surface of the piece that do most of the stretching and compressing. This means that, all else equal, a thicker, or deeper, piece will be stiffer. We all know that, of course, but it's well to keep it in mind. For one thing, the piece gets disproportionally stiffer as you make it deeper; all else equal the stiffness will go as the cube of the thickness of a top, or the depth of a brace. A low density piece of wood that has a low E value can still end up making a light top if adding thickness brings the stiffness up without making it too heavy.
What this says, then, is that we're most interested in the relationship between Young's modulus for extension along the grain and density. These are relatively easy things to measure. If you look at these for a lot of different kinds of wood you start to see some interesting things.
One is that hardwoods often don't genrally have E values that are much higher than those of softwoods, but the hardwoods are usually denser, and often much denser. This means that hardwood tops, when worked to the correct stiffness for a guitar top tend to be much heavier. This is not universally true, of course. For one thing, hardwoods are more variable in their structure and properties than softwoods, and some of them are notably low in density with reasonably high E values. Balsa is technically a hardwood, for example, and has been made into very light instrument soundboards. Of course, it has drawbacks, particularly low surface hardness. Still, in general, if you're looking at common hardwoods you'd be hard pressed to find one that would make a soundboard as light as most softwoods. To put a number on it, most rosewood samples I've tested have had long-grain E values on the high side of the range I've seen in spruce, but the rosewoods are at least twice as dense, and some, such as Morado and African Blackwood, as much as four times.
Compared with hardwoods, softwoods are all structurally quite similar, which means that they tend to vary less in terms of the properties we're looking at. Granted, individual pieces of softwood can vary a lot in density, but it turns out that the relationship between Young's modulus and density doesn't vary much across softwood species. What that means is that if you want to make a light weight guitar top you can use just about any species of softwood, so long as the density is reasonably low.
To put some numbers on that:
The softwood samples I've measured range in density from about 300 kg/cubic meter to around 550 k/m^3. The E values at the low end of the density scale cluster around 6000 MegaPascals, while the densest samples are close to 19,000MPa. When I chart them out, and draw a straight line between those values, I find that something like 60% of all the samples measured fall within 10% plus or minus of that line.
Different species of soft woods tend to have different densities. Western Red Cedar tends to be the least dense of the 'usual suspects' I've tested, with Engelmann being next up in the scale. That's followed by European spruce, Sitka spruce, Redwood, and Red spruce, in order. Those are the only ones I have large enough numbers of samples for to be reasonably confident of the averages. At the same time, I'll note that there's a LOT of variation within any species. The densest samples of softwood in my data are a couple of pieces of European spruce, I have Red spruce samples that have density as low as WRC, and so on. The moral here is that the only way to know the properties of a piece of wood is to measure it.
Along with the usual suspects, I have tested quite a number of 'alternative' softwoods. Often I have seen only one or a few samples of any of those, but, for the most part, they follow the same rule relating E and density. Of these I, and may students, have used at least a half dozen for guitars, and all have worked out about as expected given the measured properties. These include several spruce species, such as White spruce, Lutz spruce, and so on, as well as White pine, Western hemlock, and Douglas fir.
All of this assumes that a maker can, and will, vary the thickness of the top to obtain the 'correct' stiffness, whatever that is. Given the way stiffness and thickness are related, a thick top of low density can weigh less than a thinner one of high density wood, as has been said. It's fairly easy to solve the equations that tell you how much a given sample of top wood would weight when worked to that stiffness. It turns out that, in general, the lowest density tops will be about 25% lighter than the highest density ones. This is a useful difference: 'sandwich' tops tend to be about 40% lighter than ones of 'standard' construction, and that accounts for the added power.
Again, cross grain stiffness does not seem to be as important as long grain in the long run. Also, cross grain stiffness is far more variable, being chiefly predicted by the angle of the annual ring lines to the face. Since this can vary a lot even within a single piece, and the loss of cross stiffness for a small deviation from 'perfect' quarter can be large it's something that has to be dealt with top by top.
It is hard to say what effect damping has on tone. Part of the reason for this is that damping is less straightforward to measure than density and E. For one thing, it varies with frequency, and may do so differently for different species. Wright's modeling study included damping as a variable, and found no significant effect from changing the damping by a factor of three.
Steel string guitar groups on line in particular abound with threads trying to describe the tonal differences between different spruce species. Often this devolves into a 'wine tasting' discussion, with subtle subjective perceptions being given the weight of gospel. As somebody who has tried to make 'matched pairs' of guitars that sound the same (without success as yet), I can say that even matching everything one can think of to within a few percent still results in instruments that sound different, and the scale of the differences is pretty much in the 'wine tasting' range.
Finally; it's my belief that guitars are physical objects that obey physical laws. If it can't be measured it's not there. This doesn't mean we know everything that we should measure, or that the measurements will be easy. What it does mean is that I'm not going to spend time talking about leprechauns; the world is complicated enough without them.