Romans crucified according to what they found in the area. So it all depends.
Only one crucified individual has been found in Israel: A man called Jehohanan, who was killed in the first century. His remains show shards of olive wood. As he was crucified on olive wood, it would have been quite a short cross, as olive trees aren't that tall - slightly above eye level being about as high as one can expect. The Romans always used local wood to crucify, so Akasia or Olive wood or such, would have been used. Therefore Jesus' cross would not have been very tall.
Similarly, the Romans didn't always nail people the same way. The soldiers sometimes nailed them in odd positions for fun. They also tended to pry the nails out afterwards to save iron (confirmed in the excavation of Jehohanan).
It was also usually the case that criminals only carried the cross-bar, not the upright as well. This would then be notched into place on an already set-up pole. This would especially be expected in a normal crucifixion, which would take place at well known execution areas. Only in special cases, such as when Titus took Jerusalem and ran out of wood for crucifixions, were the uprights set up then too. Likely Jesus was just raised by a sort of pulley system onto an already present pole, after being nailed to the cross-bar. His feet would then have been nailed onto the footrest while already on the cross, which is further support for the cross not being too high.
Alternately, if Pilate rushed his execution and the usual crosses were already full, he might have forced Jesus to carry the whole thing, but as the soldiers already had Simon of Cyrene help him, it is unlikely they would have forced him to dig the hole also. It would likely have been a prepared hole they slotted it into. The Romans also crucified people onto trees on occasion, so there is that possibility as well, that His crossbar was simply raised onto a tree. This would fit the Talmud's possible reference of Yeshu on the Tree.
