which solution is potentially more hazardous to your eyes: .1M HCl or .1M NaOH? Why?

are they equally hazardous since one is an extremely strong acid and one is an extremely strong base?

Both are extremely hazardous and you certainly don't want to get EITHER in your eyes. The NaOH is worse, however, because it acts on the protein of the eye almost instantly as a coagulating agent much like cooking an egg white.