A better example would be american football vs rugby. One being a variation of the other, but both with minimal protection gear. American football evolved into something where one has to wear full combat gear, supposedly for protection purpose, while the style also turned to a full combat sport. All the extra head protection resulted in play techniques that are unsee in rugby, along with the high prevalence of CTE among players.
At least on the college level, rugby players are much more likely to be injured. Rugby players are 2.5 times as likely to suffer a concussion.
Comparison of Injuries in American Collegiate Football and Club Rugby: A Prospective Cohort Study - PubMed
Overall injury rates were substantially higher in collegiate rugby compared with football. Similarities between sports were observed in the most common injury types (sprains and concussions), locations (lower extremity and head), and mechanisms (direct player contact). Upper extremity injuries...
As a rugby fan this does not surprise me. The referees are very careful about calling dangerous tackles, but there is still a lot of unintentional harmful contact.
Rugby is a MUCH more entertaining sport to watch than American football, however.