jämför med ELLER likna vid?
Can somebody please explain what's the best way to use these phrases? I have looked them up and discovered that both of them can be translated as COMPARE.
here is the sentence I've tried to invent:
När vi jämför den svenska flaggan vid den ukrainska flaggan ska vi se, att de har samma färger, men olika mönster.

Question

jämför med ELLER likna vid?
Can somebody please explain what's the best way to use these phrases? I have looked them up and discovered that both of them can be translated as COMPARE. 
here is the sentence I've tried to invent:
När vi jämför den svenska flaggan vid den ukrainska flaggan ska vi se, att de har samma färger, men olika mönster.

Answer

It's pretty easy: "likna vid" is only used for metaphors (puts stress on similarities), "jämföra med" for comparisons (puts stress on differences)!
 - Statsministern liknade Sverigedemokraterna vid NSDAP. 
The prime minister compared (insinuated similarities between) the Sweden Democrats to the NSDAP.
 - Det är svårt att jämföra löner i Sverige och USA eftersom skattesystemen är helt olika.
It's hard to compare salaries in Sweden and the US since the fiscal systems are totally different.