This is an interesting question. But first things first, you should be specific in what you meant by “more dangerous”. If you meant that AC has been causing more deaths per year than DC, then it is just self-evident. Virtually all electrical appliances in our everyday life work with AC rather than DC, and those DC appliances are mostly only powered by external batteries with a voltage well below the Separated Extra-Low Voltage, or SELV, which is considered generally safe for humans. Therefore, it is quite understandable that there are more accidents with AC than with DC.
But in another sense, and I assume that this is also what you really meant by “more dangerous”, alternating current is indeed more likely to cause severe damages to human bodies than direct current under the same conditions, that is, conditions like the weight and height of the victim, exposed body parts, duration, air humidity, and most importantly, current and voltage.
And here comes the tricky one: measuring the voltage of alternating current is not as straightforward as direct current, because alternating current, by definition, is always regularly changing its voltage and direction. If we depict the voltage changes of AC and DC in diagrams, DC can just be represented as a simple level line, meaning the voltage of DC doesn’t change with time and always remain constant, while the line representing AC will be sinusoidal, or in another word, wavelike, because AC doesn’t have a constant voltage or direction. Normally, when we speak of the voltage of AC, we mean the root mean square (RMS) of it, not the peak value. The RMS voltage of AC is calculated by dividing the peak value by the square root of 2. So when we say that household power supply is 120 volt, we are talking about RMS voltage. The peak voltage of household power would be roughly 170. This is one reason why AC might be more deadly than DC at the “same” voltage.
Another major reason why AC is more dangerous than DC is that alternating current is always changing direction: it doesn’t flow towards the same direction like DC does but regularly switches into the opposite direction. Now it may sound counterintuitive to you. You may think that if the current first flows towards one direction and then switches to the opposite, there should be no energy left. But electricity is not like water. If the water inside the water pipe always shifts its direction, you would certainly go nuts, because then there would be no constant water flow coming out of the tap. However, electrical energy comes from the movement of electrons rather than the electrons themselves. So as long as the electrons keep moving along the wire, it doesn’t matter which way they are going. Or it does matter after all, if what we are concerned about are electrical accidents. You see, human bodies have a fair amount of impedance for electrical current, which is why we can endure extra-low voltage current. But if the electrical current constantly changes its direction, our body’s impedance for it would decrease. And the more frequent the changes, the less our impedance. While the frequency of household AC electricity is 60 Hz in the US and 50 Hz elsewhere, the frequency of DC electricity is 0 Hz anywhere, because it never changes direction. Therefore, we would generally have lower impedance for AC, thus increasing the risk of danger.
These are what I believe the two major reasons why AC is more dangerous than DC. For further reference, you can also check out this website: http://www.highvoltageconnection.com/articles/ElectricShockQuestions.htm