One thing that will help in your research is to realize that Japanese Jujutsu is not a style. It's an extensive family of arts, none of which is named just "Japanese Jujutsu."
Generally speaking, you can divide that family into two large divisions.
Koryu (old school) arts are those created before 1868. They generally carry a lot of cultural trappings which would seem foreign to most modern students (even modern Japanese). Koryu jujutsu styles are pretty diverse in terms of their content: some were designed for civilian use, some for the battlefield. They will have an approach to training which is very different from BJ or most other modern arts. Koryu schools are hard to find and very selective regarding who they will allow to join. Here's a video for Takenouchi Ryu, one of the oldest surviving schools of jujutsu:
Gendai (modern) arts are those created from 1868 on. There aren't a lot of extant gendai Japanese arts which still use the "jujutsu" moniker. The most widespread Japanese gendai arts from the jujutsu family are Judo and Aikido, both of which have discarded the jujutsu name, but absolutely come from that family. There's also Daito Ryu Aikijujutsu (the parent art of Aikido), which presents itself as koryu, but was probably created in the modern era. There are also jujutsu arts taught within the Bujinkan and its derivatives (Genbukan, Jinenkan, etc). These arts go back to the koryu era but are usually not taught in such a traditional way. One of our members,
@gpseymour, teaches a gendai system (Nihon Goshin Aikido) which was created in Japan but has since gone extinct there and is only taught outside that country. Wado Ryu is a Japanese karate style which is really just as much a jujutsu style. (It was created as a blend of karate and jujutsu and originally was named Shinshu Wadoryu Karate-Jujutsu.)
Most schools in the West which bill themselves as "Japanese Jujutsu" are actually teaching systems of jujutsu which were developed outside of Japan, just as BJJ was. Most often these were derived from Judo (as BJJ was originally) and/or Aikido, with possible influences from other arts such as Karate. Danzan ryu is a popular system which could at least make a credible claim to being "Japanese" in that it was founded by a Japanese man. However, he did so while living in Hawaii and incorporated elements of non-Japanese arts such as Lua, Escrima, Boxing, and wrestling. A better description would be "Japanese-American jujutsu." Danzan Ryu has a number of spin-off arts such as Small Circle Jujutsu.
Danzan Ryu:
Small Circle Jujutsu:
The degree to which a jujutsu school will work your cardio and your grips will largely depend on how much time they dedicate to Judo/BJJ style live randori. That will range from "not at all" to "all the time."
