Are we seriously debating whether Pillar would be the leadoff hitter? WTF. He's a below average hitter in every respect. Even if he makes a big improvement, he likely goes from a 93 wRC+ hitter to a league average hitter.
Tulo is one year removed from a .432 OBP, 170 wRC+ season (.391 OBP, 141 wRC+ in 2013) Pillar couldn't touch that level of excellence in his wet dreams. Unless you think Tulo is completely done as a hitter, with no chance to rebound, then any logical person wants Tulo getting more at bats than Pillar.