To strive means: to reach for, to aspire towards, to aim for etc etc To struggle means : to fight towards, to wrestle with etc etc. Struggle implies that it is difficult or a challenge I strive towards perfection when I'm learning to speak Croatian - but I have to struggle every day with nouns and their declensions. Barbara strives to be really good at speaking English but sometimes it seems so complicated that she struggles to find the right word to use :-) :-)

They are not synonyms. To struggle means you will not enjoy it. To strive means you reach for something, but it could be enjoyable or unenjoyable. I strive for more free time in my day. I struggle through a difficult math test.