With intersect, you will find the matching one string*:
>> sstr1=strsplit(str1,' ');
>> sstr2=strsplit(str2,' ');
>> intersect(sstr1,sstr2)
ans =
'Congo'
However, I'm not sure if that's really what you want - if you compare "Democratic Republic of the Congo" with "People's Republic of China", you will also get some nonempty result.
*Please note that I have an older Matlab release which does not include the strsplit function. However, I have a self-written one (which follows a little different syntax). In case the string splitting in my code does not work, it's for that reason.
