The current and the old capitol, based in Baton Rouge, are covered here. Even though they aren't colocated, they are just a short drive down the street.
Current Louisiana State Capitol: Cool art deco style with n observation deck at the top. Tallest capitol building in the country. Former governor turned senator, Huey P. Long, was assassinated in the hallway in 1935 for supposed gerrymandering districts to keep opponents out of office. The state supreme court has been required by the legislature to be located in New Orleans since 1898, so don't look for their chambers in the capitol building.
I went through self-guided. Little information provided. Little guidance about what to see or where to go. If you want to do some research ahead of time, start with Louisiana Capitol and History Tour leaflet from the Louisiana State House of Representatives. It's not a great resource but it's more than you'll get when you arrive if you aren't on a docent guided tour.
There was some renovation going on. The Senate Chamber was open but work was being done and the House Chamber was closed. Was in and out in about 15 minutes.
Old Louisiana State Capitol: A museum with displays about Louisiana statehood and previous capitol buildings. The pistol used to Carl Weiss to kill Huey P. Long is on display here.
