It's my understanding that some Sephardic Jews (Spain and the ME) will use lamb, but that Ashkenazi Jews (from Germany/Eastern Europe) do not. The afikomen replaces the lamb. Since most NY Jews are Ashkenazi, I never knew anyone who eats lamb for the Passover Seder meal.
That is mostly correct (though Middle Eastern Jews are a mixture of Sephardim and Mizrahim). Almost all Jews in the US are predominatly Ashkenazim, though a few "tout" a bit of Sephardic blood
They indeed have lots of differences. Ashkenazim hold as forbidden many foods that the Sephardim use in their Haggadah (Passover) meal. (e.g. whether kitniyos are banned, and what exactly are kitniyos). There is no blessing said over the 2nd and 4th cup of wine. Also the Book of Zorah and Q'ballah figure heavily in many Sephardic Passovers.
Some Sephardim allow lamb as the feature dish. Some have it, but do not eat it. Others do not permit it. Ashkenazic Jews (which means almost all Jews in the US and Europe) forbid lamb in Passover. The problem with speaking of the "Sephardim" is that after they left Portugal and Spain they mixed with the various Mizrahim communities and have, therefore, varying customs and even interpretations of the law. Yemenite Jews, for example, have many peculiar practices with Passover that differ from the Mizrahim of Egypt (where Sephardic influence was greater...Rabbi Moses anyone?). And then there are the odd Netherland Sephardim
And of course you have the outliers- the Beth Israel, who still offer animal sacrifices (and were accepted as Jewish by the Rabbis in Israel) and the "heretics", the anti rabbinical Karaites. Who is to say that there seder is not the closest to ancient Judaism?
The Karaites reject the Talmud and other rabbinical traditions. And they hold to the Tanach. Their seder is very different than that of rabbinical Judaism. They don't even have any wine!! They do have lamb though.