To start, since the subject is yeshivos, they have a different derech halimud. The Litvish put more emphasis on lomdus, the Chassidim more on b’kius and halachah. Of course, the Litvish don’t learn Chassidus.
There is a difference in mehalech hachaim. The Litvish tend to be more analytical and less emotional than Chassidim in their avodas Hashem.
The Litvish also tend to be less insular.
The Litvish also put a stronger emphasis on limud Torah than Chassidim, and the Chassidim more emphasis on tefillah, and probably more on chessed, than do the Litvish. That’s related to emotional/analytical mentioned above.
The chossid/Rebbe relationship is more important than the talmid/Rosh Hayeshiva relationship. Related to this is how to approach “daas Torah”.
All of this is still true, despite the fact that the two groups are much closer in these areas than they were hundreds of years ago.