Judaism, and early Christianity after it, always were what you could call 'mystical'. Why is 'Eastern' Christianity more mystical? Because it's the original Christianity.
Many of the spirituality we associate with 'Western' Christianity developped after the schism. For example, there is no record of any stigmatics before Francis of Assisi... Scholasticism, obsession with visions, and other parts of Western spirituality came after the schism. It's pretty clear that before the schism, Western spirituality was much closer to the Eastern, more 'mystical' faith...
Now, to get back to the original question:
I think alot of it has to do with Rome's need for 'proof'.
Leading up to the schism, Rome started making claims of it's universal jurisdiction over all of Christendom. But these claims had no basis, so they started coming up with all sorts of fabricated 'proof' to back up their claims. Forged documents like the Donation of Constantine, a robber council (which was overturned), claims of Peter's supremacy over the apostles (conveniently forgetting Peter was also Bishop of Antioch), etc... Rome has never ceased trying to 'prove' their position.
This attitude seems to have crossed over into their faith as well. Stigmata is 'proof' of one's holiness, visions are used as 'proof' of doctrines, spirituality, etc... And they even needed to intellectualize their faith to 'prove' it's validity to our human reasoning. And of course, this attitude didn't stay with Rome - as the protestants were the offshoot of the Roman church, they also inherited this attitude... Many of them abuse scripture to try to 'prove' their own positions, many of them use junk science to try to 'prove' God's existence, etc...
Why has this never developped in the East? Because there's never been any doubt the Orthodox church is truly the 'One Holy Catholic and Apostolic Church', and there's no doubt our faith is the true faith.