Census shows William B Houston as the younger of these two men, age 17 in 1860. He would have been old enought to enlist in the "Beck Rifles" by 1861.
Houston's company commander listed him among the survivors of the first day's battle. As reported in his service file (which lists all battles and skirmishes in which he was present), WBH was killed in the great attack of July 3rd, 1863.

Copies of both services files may be obtained here.