Dissolving Organic Tissues
I would say that acids are better.

Why? Bases and acids dissolve flesh pretty easily (I'm thinking of $\ce{NaOH}$ and $\ce{HCl}$ here, weaker acids/bases -- not so much). Most of our body is made up of proteins, which are overall pretty much neutral (generally). Both acids and bases can dissolve protein.

On the other hand, there is one major component of our body which is easier to dissolve with acid. Bones. The major component of bone is $\ce{CaCO3}$. The reaction $\ce{2HCl +CaCO3 -&gt; H2O + CO2 ^ + CaCl2}$ is much more efficient/faster than $\ce{2NaOH + CaCO3 -&gt; Na2CO3 + Ca(OH)2}$. Why is this? Well, for one, in the acid reaction, a gas is being released. This speeds up the reaction, by Le Châtelier's principle. 

Apparently, NaOH is not able to dissolve bone completely, you are left with a fragile shell. Either way, it will be much slower than $\ce{HCl}$ while dissolving bone.

Here's an interesting article (no claims on validity) of why lime shouldn't be used to dissolve a corpse.



While (as far as I can tell) acids may be the better way to dissolve a body, I feel that filmmakers use acids because the term is known to most of the general public (unlike "bases", which isn't)