US is a huge territory, and differences in suicide rates vary quite much across both Europe and the US by region. Finland has only marginally higher suicide rate than US (14.8 vs 12.1) if you consider that Alaska and many states in the Western US have rates around and above 20.0 (per 100,000): http://afsp.org/about-suicide/suicide-statistics/

Rates of homelessness:

US: 633782 / 314000000 => 202 homeless per 100,000

Finland: 7877 / 5363000 => 147 homeless per 100,000

Based off of numbers from (YMMV):

http://www.housingfirst.fi/en/housing_first/homelessness_in_...

https://en.wikipedia.org/wiki/Homelessness_in_the_United_Sta...

https://www.google.com/?gws_rd=ssl#q=population+of+usa+in+20...

https://www.google.com/?gws_rd=ssl#q=population+of+finland+i...

I think having a basic income would do more than ensure people have a place to live, as the social welfare system you mentioned gives them; it'd guarantee a minimum of dignity. People in homeless housing/shelters are certainly better off than in the streets, but, imagining myself in their position, I think I'd still feel like an outcast, out of step with the rest of society. If there was a way to give people a base level of dignity directly, that'd be the way to go, but I think basic income is an interesting avenue to try to do this.