What is the most similar war to WWI?

This depends a great deal on what aspect of WWI you are
going to focus on.

To me, the war that was most like WWI
was the American Civil War.  That is because the Civil War was the other major war in
which there was a great deal of trench warfare and many episodes of offenses trying to
storm very strong defensive positions.

Both the Civil War
and WWI were industrial wars before tactics had adapted.  In both wars, the
technological levels of the time strongly favored defense.  The defenders could decimate
armies that staged frontal assaults.  Even so, the offensive tactical doctrines had not
yet evolved to the point that frontal assaults were
abandoned.

Because of these factors, both of these wars
were similar in that both involved huge numbers of casualties incurred by frontal
assaults on strong defensive positions.