Why not both?  Science and healing.  I have seen both and I know Christians who are doctors and use medicine.  I think it is crazy when someone throughs away a pill bottle and says I am going to believe God is going to heal me and then they end up dying.  But I have also seen people healed without medicine and people praying for them, even things like arthritus.  I think the stand that I have heard some Christian people take is that medicine does not heal anyone, it just gets your body to the point where it can heal itself.  I do have to disagree agree with you though.  I think more have been healed by Jesus than by medicine.  That is just my personal experience and what I have witnessed and I am also including in that things like drug addiction, sexual molestation etc...  I have never saw a pill totally transform a person, but I have seen Jesus do it.  There is also four layers (maybe more)  that I have found in the bible about healing and sometimes people intertwine them.  1) Healing by your own faith.  This one can grow and it is based on your faith, not God's but the faith He has given you and it can grow, but takes a lot of work.  2) Healing by God.  This is when God heals someone right out of the blue.  They could just be walking down the street and suddenly they are healed.  They usually feel or have an encounter with God during this. 3) Healing by word/Spirit of knowlege.  This is when you know what is wrong with someone without them telling you.  Like you know so and so has cancer or something that happened in their childhood and you then heal them.  You usually pray or command what it is you have seen to usually leave or dissolve.  This difference between a word of knowlege and the Spirit of knowlege is that the  Spirit of knowlege is more like a river and not just one word.

You may seem to know a great amount of detail about someone and it keeps flowing out. 4) God's presence.  You will sometimes be healed by feeling God's Glory.  This is what would happen with Peter in the bible when he walked by people.

I think force of will and positive thinking have a great deal to do with getting better, physically or psychologically. Call it whatever you want.