Your old windows probably had a built in flange and did not need to be caulked to the J channel.
The new inserts do not have that and need to be sealed to the J channel.
I would just add that it really depends on the exact circumstances... In fact I have seen far too many replacements installed where the new capping is installed over the drip cap and the caulk to the vinyl. That is a major no-no. I diagnose leaks on those installs on a regular basis. Vinyl siding is design to allow moisture behind it, and caulking that to the window or trim in some cases will direct water right into the window opening.
I know that you are aware of that danger anthony, but I just wanted to clarify it for the OP and others who may view this.
I'm going to agree with HS here. Far too many installers think that caulk is a do all end all seal. It's not.
OP I like the foam wraps on the windows, as long as both inside and outsides are sealed. The size of the gap is the determining factor for us. If I can fit the nose of my foam gun in the gap, I use foam, If, as in most cases the window is measured tight (commonly referred to as goodntight)
then we use caulking. :