Two areas where differences are quite evident are with regard to drinking (עד דלא ידע), and the view of the special nature of the day with regard to davening and ישועות.
What is the preeminent position of the great Litvishe גדולי ישראל re imbibing on Purim?
In the current issue of Yated Ne'eman (USA), we learn the following of the Purim conduct of מרן ר' אהרן לייב שטיינמאן ז"ל.
1) Rav Aharon Leib drank more than usual, even more than one becher-full of wine (note - not even two bechers, just more than one. So in reality not much.) (p.50).
2) Rav Aharon Leib chastised a talmid who had already had too much to drink, but sought dispensation to drink more, by asking him, do you really want to become drunk? Did Rav Shach do so? The Brisker Rav? The Chazon Ish? (p.52)
Earlier in the same issue (p.48), we are told that after a certain incident The Steipler ז"ל resolved that he would not drink excessively even on Purim.
From the USA and Slabodka, another Litvishe gadol, Rav Avigdor Miller ז"ל, spoke out very strongly against inappropriate excessive Purim drinking as well. See here and here, for example.
So there you have a row of great Litvishe leaders of our era that strongly put the brakes on taking the inyan of עד דלא ידע too far. More examples exist of course, but I am sticking to easily available written testimony here.
On the other hand, among some Chasidim, the matter is viewed differently, and sometimes they drink עד הקאה, ועד בכלל, ואפילו יותר (for more on this, including very strong quotes from a Karliner Rebbe and the Nesivos Shalom of Slonim, see the section מספר חכמים יהודיים שדווקא תמכו בהשתכרות בפורים here. Also, note the ninth comment after the post there by בצלאל א about extreme Purim drinking in Breslov.)
Davening on Purim - Not a blank check
Another ענין where confusion is rampant is with regard to davening on Purim. Many promote ideas that on Purim a person can ask anything of Hashem (which can be done all year actually), and give the impression that one is assured to get anything requested through davening on that great day. On the other hand, a Litvishe view is that while תענית אסתר and/or Purim are enhanced ימי רצון for תפילה, there is no absolute guarantee that one will get what one davens for, even then. רחמנא ליבא בעי.
As time goes by, occasionally we see that some Litvishe have come under Chasidic influence in these areas. That is due to more mixing between the groups, such as Litvishe people davening in Chasidic places, marriages between the groups, and other interaction. They are therefore left confused about such things. Which is why educational initiatives such as this are important.
May Hashem help us keep to our דרכים, under the leadership of our גדולי עולם, and in that זכות we should be zoche to רפואות, ישועות, וגאולות.
א פרייליכען פורים
P.S. Important past Purim related posts are still here for חזרה. For example,