This seems like a good first post for me to make here, having worked as a power engineer before, sorry if it's an overly complex explanation.
As color_me_gone said, the tall transmission towers operate at a voltage up to 750kV in north america, a bit lower in Europe. I would say with the currents involved in that transmission level is enough to cause severe burning and in most cases death, but it will be very tricky to cause a short circuit, or arcing, due to the spacings of the live wires, as more safety clearance is given in the higher voltage networks. Also, depending on the location where you are there is a not insignificant risk of being spotted climbing a tower and consequently the circuit being switched off, although I can't say how it is monitored in North America (i.e if they are remote enough). And I think it is extremely rare to succeed with the big transmisson towers, I've only seen reports of someone attempting to climb towers.
The summary is, it's risky to do with the biggers towers, and it is also "overkill" with the currents involved. Even, say, a 33kV voltage will cause similar results (Which are usually the bigger wooden pole ones, but a lot smaller than the big transmission voltages), where making a connection between two of the lines causes a short (they usually have 3 or 6 live wires), which are not that far apart.
Though for the peacefulness of the method, I would be doubtful like it has been said. It's likely that the amount of current would be enough to be lethal, but there is a risk that it is not, and then the consequences of severe amount of burning and other potential damage like PoisonousPotato said would be pretty bad, which is likely an understatement.
