From a tech note by our friends at Mesa-Boogie discussing the differences between EL-34 and 6L6 power tubes:
Technically speaking, EL-34s are served higher voltages and utilize more current than their 6L6 counterparts. Non-technically, they run hotter! This hotter/higher-current operation is one of the reasons why EL-34 tubes (and the amps that use them) offer such a wide range of overdrive.