Hinn's criticism is pretty common. I've certainly heard it before.
So, the reason why we use these standard prayers is because we know they work. In the case of the Lord's Prayer, it was clearly given to humanity by Christ himself. There is an excellent reason for us saying them. That being said, I know that when I was growing up Catholic, there was definitely a temptation for me to simply say Hail Marys and Our Fathers and call it a day. I was saying the right words, but without much intentionality behind them. So I get that part of Hinn's criticism.
I think he is wrong for a couple of reasons, though. The positive thing you have to say is that Orthodox spirituality has an ancient tradition of prayer and mysticism that is beyond anything else in the world. In fact, Orthodox mysticism is what first caught my eye as a Catholic. Even though there are Catholic mystics, it is not uncommon today to have Catholic schools and clergy recommending Orthodox literature for those pursuing spirituality and mysticism. Look at the dispute between St. Gregory Palamas and Barlaam. It would be hard to argue there is any Christian church that puts a higher value on mysticism and communion with God than the Orthodox Church.
On the negative side, one of the arguments I've heard articulated against Hinn-type prayer is that it can be rather Pharisaical. Jesus told us to shut the door and pray in private, not loudly speaking in public in an overwrought manner. If you want a really horrifying example of Pharisaical prayer, find Gov. Rick Perry's "prayer" at his rally in the Houston stadium. Really a sad example of someone using "prayer" as a commercial.
To tie it all together, Orthodox are taught to value and use the standard prayers we have received from Jesus, the Bible, and tradition. When we are still learning to pray, these prayers keep us from error. Some of the commonest errors, in turn, are focusing only on our own needs and praying demonstratively in the way Jesus cautioned us against. Orthodoxy does not, however, exclude anyone from praying in a more personal, "charismatic" manner.