I would submit that the 1st Battle of Manasass (Bull Run)was one of the most influential.

While it did not have the "Grand magnitude" of the later battles, at the time it was the largest and most costly land Battle fought on American soil. And set the tone for the continuation of the rest of the war. Both the North and the South thought that other side would be a push over.

Also you have to consider the battles of Fort Henry and Fort Donelson, which open the Tennessee River to the Union forces and thereby most of Tennessee came under Union control. While nothing fantastic as far as "shots fired", it was the first "crowning glory", on the path of success, of a little know man by the name of U. S. Grant.

There are many ways in which a particular Battle can be determined to be significant or Influential. Large numbers of troops and grand battles of manuver are attention getters, but that alone does not necessarily make a battle significant in my opinion. For example the Battle of Shiloh would not have happened if the fall of Forts Henry and Donelson had not happened first.

So which was the more significant Battle? To me Shiloh, though grander in scale, was mearly a followup and the result of the success previously achieve by the earlier victories at Forts Henry and Donelson.