47/53, as tom says, is about as good as you can get on a tri bike. this, because of the steeper seat angle and the fact that you’re laying your torso on the front of your bike.
60/40 on a road bike is great in theory, but you can’t get this if your hands are on the drops and you’re riding on the rivet. 60/40 becomes 55/45 becomes 52/48, and so forth, depending on where you sit.
put your rear wheel in your trainer, the front wheel on a scale, level the bike, and move around on the saddle and the handlebars. you’ll see how weight distribution changes.
personally, i don’t think tri bike handling is a big problem when you’re in the aero position. it’s when you’re out of it that the problems can occur. i think ashburn’s right, if you can ride no hands you’re in pretty good shape.
at the same, time (and i have no good math for this) i think the problem isn’t simply weight distribution over the wheels per se, but how much weight sits in front of the steering axis. when you’ve got a big aero bar out there, and your hands are out there, and if the stem is long, and the distance between the stem clamp and the hand-hold position on the pursuits is long, then you have a lot of what gerard calls “tiller” and you also have a lot of weight on that tiller.
the steeper your seat angle, the more weight is on that tiller. if your pursuit bars are angled down, you have even more weight on the tiller. while descending, even more weight. while braking, even more weight. and so forth.
again, i’ve got no good math on this, but i think the pressure on a system to oscillate increases, and the ability of a system to resist an oscillation once started decreases, as more and more force is applied to the steering axis (and more leverage increases that force). accordingly, if your wheel isn’t exactly true or the rim is the least bit wavy in its construction, you get speed wobble when you brake. or you just get wobble at a certain speed, braking or not.
of course, speed wobble is an issue unto itself and one can spend a lot of time on this (without ever coming to a concrete set of answers) but i think BOTH weight distribution AND the force applied to the “lever” attached to the steer column contributes.
one last thing. i mentioned that this is more a problem when NOT in the aero position. when you ARE in the aero position your weight is resting on a place much closer to the steering axis (almost right on top of it). when your hands are on your pursuits, next to your brakes, this dynamic changes for the worse. i’m not saying you shouldn’t be on the pursuits when in dicey situations, i’m just saying that problems often tend to manifest themselves on tri bikes with hands on the pursuits, while descending, while braking, and this is the triple whammy that places a ton of weight forward of the steering axis.