We do not use either, we use standard wire nuts.
The greenies would not e very helpful as most of our grounds are fully insulated.
IMO the "Term-A-Nuts" are not worth the money they cost. They do look great and are easy to use.
I have not installed a barrel crimp in 20 years, I never liked them, IMO when you use them with a group of 12 AWG solid the crimp loosens when you push the wires back in the box, IMO they make a lousy connection.
If space in the box is that tight I suggest roughing with larger boxes.