I won't speak on behaf of BJJ but for wrestling:
If you live in America you can start as early as 3 years old and support continues as long as you want to compete in most cities. Free. Access to diff styles (folk, free, and greco)
Wrestling is about controling your opponent. Wrestling teachs you takedowns, clinch, stopping takedowns. Wrestlers tend to be top notch scramblers. Wrestlers tend to have great condtioning. Wrestlers tend to alwasy be on weight.
weaknesses tho involve not really about finishing opponent. wont help you with multiple attackers. bc other than takedowns it is more defensive oriented than offensive size difference comes into play more so than bjj.
So depends on the application on which one will work best for you.