1. The outward appearance (hats, frocks, peyos, black and white, etc.)
2. Their stance on Zionism. Although they are probably the most lenient with Zionism in comparison to other “chareidi” factions, they still harbor a somewhat hostile view towards the state. If you look at the writings of countless Sefardish rabbonim in the past, they had an affinity to the idea of the State. This is a fact.
3. The kollel system. This is a modern, Ashkenazic invention. By kollel system I mean that people en masse do not work and instead learn long term. This NEVER existed in Sephardic lands. There were yechidim who did that but by and large, parnasa was encouraged. Even Rabbonim worked.
4. Adopting more machmir approaches to Halacha like the Litvish tend to do.
There are other examples but these are the main ones. The reason we like Shas is because we relate to it. We relate to it because it was copied from us.
No one should get offended from this. People should just realize that the Litvish derech is not universal. There are other ways of thinking.