Haven't found the overall rate for Europe, but this is pretty interesting:

http://www.rferl.org/features/2002/04/09042002073543.asp

Seems like the Baltic countries have a rate 4 times the world average. Tied to the high sales of the Blue Oyster cult hit "Don't Fear the Reaper", no doubt. 'Cause it's not like the Euros have guns.

Worldwide Male suicide rate charting tool here. Doesn't give stats on women; men are roughly double women in most places. I plotted Europe, it's pretty damn grim.

http://www.nationmaster.com/graph-T/hea_sui_rat_mal&int=-1&id=EUR

US stats are pretty much on par with Europe:

"The survey found that in the U.S., mental disorders are quite common; 26 percent of the general population reported that they had symptoms sufficient for diagnosing a mental disorder during the past 12 months. However, many of these cases are mild or will resolve without formal interventions."

http://www.nimh.nih.gov/press/mentalhealthstats.cfm

And suicide rates are probably similar per capita although I don't know that for sure. What is better in Europe is a more consistent culture against the use of pills to modify "low-grade" mental illness. With most health coverage only giving 5-10 sessions for psychologists in the US, the pressure is to medicate and get them out the door. Good for pharma, but not so great for those suffering.

If mental illness/suicide rates are similar, then I don't see counselling vs. pills being a better approach.
1. Given that Europe is more northernly than the US, perhaps much of the problem can be related to Seasonal Affected Disorder.
2. Some/much mental illness is a chemical imbalance in the brain. In those instances pills would be appropriate.

I have seen first hand when those need meds stop taking them...

Hmm. A couple of points. (1) The 26% number includes such things as simple phobias which generally have limited impact and little need for treatment. (2) Various parts of the world use different criteria for various mental illnesses, leading to something of an apples vs oranges comparison. (3) The completed suicide rate varies significantly by culture, although it appears the US and Europe are similar in that respect.

I'm not going to touch the meds vs talktherapy debate.