The biggest reason for the price difference is getting money into BTC-E is hard!
How easy/hard is it to get money out of BTC-e?
I have little experience with BTC-e and none whatsoever with Bitstamp but if this is true, then it does sound like a reasonable explanation. Back in mid-late 2013, it was much easier to get BTC out of Mt. Gox than fiat. So naturally more people exchanged their fiat into BTC and withdrew instead of exchanging their BTC into fiat and getting their withdrawal delayed. That resulted in increased demand for BTC and a BTC price that was significantly above every other exchange operating at the time. Usually these sorts of price differences between exchanges can be explained by the ease of getting fiat and BTC in and out, as well as trading and/or deposit/withdrawal fees.
I would say it's very hard.
I tried wire transfer to withdraw some fiat to my bank account, but after a few days the amount just came back to my btc-e account, and never have arrived in my actual bank account. BTC-e has currently disabled a few deposit methods as well, and the only easy way to do this is to purchase BTC-e vouchers from a third party source, which increases the rate of you being scammed and stuff.
I don't recommend trading on the website.