I guess it depends on what type of tire, and what the application is.
For sportbike/racing tires, the aspect ratio helps to determine the "turn-in" characteristics of the tire. If it has too low/wide of a profile, it is very hard to turn into a corner (hard to force the bike to lean). If it is too tall, the bike is very "skittish" at turn-in, and can be downright unstable and scary. Don't ask me how I know this.
Can you say what your application is? What range of aspect ratios do you see for the tires you are looking at?
Load capacity is usually a function of tire construction and size as opposed to aspect ratio.
To help explain berkeman's answer, for the same treadwall height, a higher aspect ratio will be more parabola like, while a lower profile will be circular or lower still like a flattened circular arc. A more parabola like profile will provide more contact area when leaned, and have less resistance to leaning over. For a given aspect ratio, a taller treadwall will flatten the profile. To a rider, the sensation of a more parabolic profile is that it takes less countersteering effort to lean the bike, and the rear end can feel like it's stepping out more, if the rear tire is wider than the front, and the tires profiles have just been changed, as a rider will acclimate to the new feel. I don't recall if you get the same sensation if the front and rear tire are the same (the last bike I had with the same front and rear tires was a 1973 Norton 850 Commando, which used parabolic profile Dunlop K81 or K181 tires, and I don't recall the sensation of the rear end stepping out).