The main, fundamental differences between Chassidus verses Yeshivish religious practice are as follows:
1. Religious practice based on sincere intent (Chassidus) vs. Religious practice based on you do… or else it’s an aveira.
2. The rebbe is definitely a spiritual leader, but its also an organizational structural difference. It is a more personalized approach. vs. Litvish rely on Gedolei Yisrael/ Gadol hador/ rosh yeshiva for mesorah. Its pretty much impossible for most litvaks to meet any of these gedolim for themselves (I live in America, the likelihood I will ever meet a gadol in Bnei brak is…).
3. The social mechitzah is different: A yeshiva bochur who is 17 when walking past a 16 year old girl on the sidewalk from a local bais yaakov on shabbos will say “gut shabbos” as a reflex. Vs. In BP, Williamsburg, a married man walking down the street will never say “gut shabbos” to a five year-old girl/ female period. They will not even respond if you ask them for directions (went through that one time and ended up inside the men’s section of Bobov-48… oops!).
4. Fervor- By the chassidim, the davening takes much longer because there is more intense concentration on each word. vs. Litvaks go more quickly.
5. Nusach: I know yeshivishe people who daven nusach sefard and others daven ashkenaz, chassidish people may daven nusach sefard, but there are other nusach sefard variations as well. Karlin-Stolin has its own siddur, as does Lubavitch, there may be others as well.