My father zatza'l, who stayed with and talked in learning with the Rogotchover, told me that by the time he got there, Reb Meir Simcha had already been niftar (Reb Meir Simcha was niftar in 1926). The Rogotchover was famous for his sharp and mordant words, and he would often say sharp things about Reb Meir Simcha as well. You realize that the Rogotchover and Reb Meir Simcha were awesome geniuses; my rosh yeshiva, Rav Rudderman, said that the Chofetz Chaim was not in the same category as Reb Meir Simcha in gadlus in Torah, and the Rogotchover was equally famous for his genius. Still, the kin'as sofrim between these very different gedolim was famous in Litteh, and the stories about them were celebrated. After Reb Meir Simcha was niftar, the bochurim tried to get him to say something sharp about Reb Meir Simcha, but he absolutely refused to say a word about him. So the bochurim had to make do with saying over the older stories. One of the stories was that two Rabbonim came to Reb Meir Simcha with a complaint: they had gone to the Rogotchover to talk in learning, or whatever they wanted to talk about, and he simply threw them out of his house. This was not uncommon; he was interested only in Torah, and if his visitors couldn't present themselves well, he would berate them and throw them out. These Rabbonim were shocked by such ill treatment- they were great talmidei chachomim, and they deserved better! Reb Meir Simcha told them, and I have to say this in Yiddish first:
.נו האי תנא ירושלמי הוא! האט ער ארויסגעוורפען צוויי יידען
What this meant was that the Gemara in the beginning of Bava Kamma asks, why does the Mishna say חב המזיק, when it should say חייב. So the Gemara answers, the Tanna of the Mishna is from Eretz Yisrael, where they use shortened words, so instead of חייב he said חב, he took out the two yuds. The Rogotchover was famous for favoring the Yerushalmi, in the path of the Rambam, so Reb Meir Simcha said that the Rogotchover learns Yerushalmi, so it's just natural that he would throw out the two Yidden.
Then there's the story about a certain friend of Reb Meir Simcha's, a great talmid chacham, with whom Reb Meir Simcha would often spend time and talk in learning. They were once in a shul, and someone spoke between mincha and maariv. The speaker knew how to learn, but was nowhere near the madreiga of these two people. Reb Meir Simcha's friend heard something in the shiur that he knew to be indefensible, and he attacked the speaker with tens of kashes, which the speaker couldn't even begin to respond to. Reb Meir Simcha got up and said, pay no attention to this man. He doesn't know the difference בין ימין ושמאל, between right and left. The baalei battim were proud that the great Reb Meir Simcha so respected their Rov, and the Rov, relieved, finished his drasha, and they davened ma'ariv.
How was he supposed to know the difference between shin and sin -- he's a Litvak!
My great-grandfather, Rav Yisrael Avraham Abba Krieger, later R' Yisrael Avraham Abba Meir Simcha Krieger, spent a number of years living with his rebbe, R' Meir Simcha haKohein miDvinsk. I had the opportunity to fly to Israel to see my maternal grandfather, his son, one last time before my grandfather's passing. He was already bedridden, and "Grandpa" spent that week telling me more interesting parts of his life story. But when discussing his father and his rebbe, you could hear the yir'ah in my grandfather's voice. It was always "HaRav Meir Simchah haKohein miDvinsk", never "he", never even "Rav Meir Simcha". And my grandfather would try to sit up while doing so. My great-grandfather, who went on to be the shtat-rav in Kashduri (Litta), the non-Austritt Kehillah in Frankfurt, and Boston (RYBS's precessor), was obviously close to the rebbetzin. After all he lived in her home from his adolescence through to his wedding day. At Rav Meir Simchah's levayah, R' Yisrael Avraham Abba took on his rebbe's names to keep them alive in his family. R' Meir Simchah had no living children at the time of his passing, and the rebbetzin was worried that the name would be lost in Israel.
Anyway, Rav Meir Simcha was known in Litta as THE rav to go to when you had Shalom Bayis issues. So, after his petirah, many many thankful couples named children after him. Which is part of the reason why he was zokheh not to really need my greatgrandfather's gesture -- Meir Simcha is a common name pair, much more so than many other rabbanim. But it did comfort the almanah, so it wasn't for naught.
Another story, more widely known, that I remembered:
A baalabos brought in his intended son-in-law to talk in learning with the Rogotchover, because he was proud that he got such a wonderful shidduch, so he wanted to show him off to the Rov. They began talking in learning, and the Rogotchover suddenly got angry and began yelling at the bachur, calling him Tzig! Goat! Amaretz! The prospective father in law was horrified, and he hurried the bachur out, and broke the shidduch. A few months later, the baalabos visited the Rogotchover again, and the Rov asked him, nu, how is your son in law, the young man you brought me last time? The baalabos asked, son in law? What son in law? When I heard you call him a Tzig, I broke the shidduch! I thought he was a talmid chacham, and when I found out he wasn't, the shidduch was off! The Rogotchover said, Naar einer, you foolish man, my goat knows how to learn ten times better than the rov in your town!