I don't know (but I think) that if you were standing in a pool of water, barefooted on a concrete floor and touched the neutral bar, you could become the better path for current to flow.
I work with high voltage, and so there are some numbers we always keep in our heads. Those of us who drink coffee all day, and then a cocktail after work, usually have very dry skin. If I grab an ohmmeter between my two hands right now, it's going to measure several hundred k-ohms. Those who properly hydrate will be much lower, in the 10's of k-ohms. If you wet your hands, you'll get down closer to 1 k-ohm, in fact 3 k-ohm seems to stick in my head from my own testing.
We probably all remember Ohm's law from high school physics class: V = i*R, which is easily rearranged as i = V/R. In this case, since we're talking AC mains power, everything is RMS voltages and currents.
If you touch anything energized, it doesn't matter whether you're a "better" or "worse" conductor to ground, as you're a parallel path to a constant voltage supply. Current will flow through you according to this i = V/R, with you being the R, say maybe 30 k-ohm. Get your hands wet, and the current that will flow though you goes up 10x, due to 3 k-ohm.
Now, you've probably heard people repeat "voltage doesn't kill, current kills". That's really kind of stupid, as you can all see you can't have one without the other. V = i*R always holds, V being voltage, and i being current. What they really mean by this is that damage to you is dictated by the amount of current flowing through you, and the amount of voltage required to create that current varies enormously by person and temperature, as there's such a huge variation in skin resistance.
The threshold for sensation is around 1-2 mA, which for someone with wet hands at 3 k-ohm, will occur around V = 1.5m*3k = 4.5 volts. For those properly-hydrated individuals not dipping their hands in water, that's going to be somewhere in the 10's of volts (e.g. 50 volts), depending on your particular skin resistance.
Going above that, there's something called the "can't let go response", which occurs around 15 mA at 60 Hz, or V = 15m*3k = 45 volts, for a really sweaty electrician. This is very dangerous, as it is exactly what it sounds like, your muscles contract and cause you to involuntarily grab the conductor, with no ability to let go. I imagine some of the professionally-trained electricians here will tell you they were taught to use the back of their hand the first time they touch a circuit, for this reason... I'm not an electrician.
Side note, residential breaker panels in our older homes of the northeastern states are often in the basement utility room, right next to a screaming-hot oil-fired boiler, so the poor electrician is always sweating while working in the panel.
These are the rough numbers to keep in your head:
Threshold of sensation: 1 mA
Maximum "harmless" current: 5 mA
"No leg go" response: 10 - 20 mA
Onset of pain: 50 mA
Ventricular fibrillation: 100 - 300 mA (varies by individual)
Burning skin: 300 mA
Note that the "no let go" response is basically a forced contraction of your muscles, so it can also cause you to stop breathing, if the current happens to be passing thru your chest from one arm to another or from an arm to a leg.
When talking about residential electrical scenarios, I suspect the only time being a "better" conductor than something else matters, is when you have something like a loose connection causing current to a circuit to be interrupted. In those cases, grabbing the wrong thing will finally allow current to flow in the circuit... through you. But the current is still limited by old i = V/R, with R being the sum of you + the rest of the circuit.
