(1) The Gemaruh says that Sirichan found on the lungs makes the animal a Terifa. There is a well known difference between Sefardim / Askenazim regarding this issue. Shulcan Aruch , Y"D,39:10, the Mechaber writes that we can't be lenient regarding these attachments to the lung, whether big or small, whether they peel off easy or not. The Rema 39:13 writes the Ashkenazi minhag is to be lenient, when it peels off easy, and it is called a " Rir " instead of a Sircha. Obviously, regarding this issue, ie. " Glatt " the Sefardim are more Makpid, and their Glatt is more Glatt, than Ashkenazim. And it would therefore be understandable why a Sefardi would not want to eat Meat ( of a cow ) in the home of an Ashkenazi. We don't stand up to their standards. The question I have is regarding the Mechaber's Lashon, Whomever is lenient regarding this issue " Is as is he feeds Treifos to Klall Yisroel ", which implies , that not only is Ashkenazi meat not Glatt, it is Treifa. Which happens to go well with our Gemaruh. Is it true , therefore, that acc. to sefardim , that not only is Ashkenazi meat not Glatt, but in fact Treif ?
(2) Regarding other differences between Sefardi / Ashkenazi Shecita :
a - Sefardim eat the heart, while Askenazim do not
b - Sefardim do Nikor of the Hind Legs ( Gid Hanashe ), and eat Fileigh Minon , while Ashkenazim somehow stopped ( it is actually an interesting question whether or not an Ashkenazi can eat from the Hind Legs that Nikor was done properly by someone who has a good Mesorah how to do it ( the Temanim, still do it ). I have asked the Rabanim of my community, and seems they are debated on the issue. We, g-d willing, will be doing a Shecita of a lamb, and are having a Temani Shocet do it, who will also be doing Nikor, and the question arose can those who are Askenazi eat from that area, and it seems to depend on who you ask )
Are there any other notable differences ???? Of course, I am not asking you if an Ashkenazi can eat meat with a Sefardi Glatt Hechsher ( that might be political ).
Being that you sound like you are from Eretz Yisrael, I can tell you that as far as I understand, all the standard Ashkenazi (including Chasidish) Mehadrin Hechsherim in Eretz Yisrael are "Glatt Beis Yosef," and you therefore have nothing to worry about. Regarding Nikur, I have no douobt that the Rabbanim you asked probably informed you of the Igros Moshe (Y.D. 2:42) who clearly says that there is no Minhag *not* to do Nikur (if it is done properly), it is simply not done as it is not convenient. This implies that an Ashkenzi could also eat the meat. I assume that the Rabbis who say it is forbidden understand that the Ashkenazim refrain from doing Nikur as it is a very complicated process which became unclear throughout the generations, establishing a Minhag not to eat from such meat.
All the best,