The energy spectrum of Markarian 421 in flaring states has been measured from 0.3 to 10 TeV using both small and large zenith angle observations with the Whipple Observatory 10 m imaging telescope. The large zenith angle technique is useful for extending spectra to high energies, and the extraction of spectra with this technique is discussed. The resulting spectrum of Markarian 421 is fitted reasonably well by a simple power law: J(E)=E−2.54 ± 0.03 ± 0.10 photons m-1 s-1 TeV-1, where the first set of errors is statistical and the second set is systematic. This is in contrast to our recently reported spectrum of Markarian 501, which over a similar energy range has substantial curvature. The differences in TeV energy spectra of gamma-ray blazars reflect both the physics of the gamma-ray production mechanism and possibly differential absorption effects at the source or in the intergalactic medium. Since Markarian 421 and Markarian 501 have almost the same redshift (0.031 and 0.033, respectively), the difference in their energy spectra must be intrinsic to the sources and not due to intergalactic absorption, assuming the intergalactic infrared background is uniform.