Presumably the instrument has been built to take larger strings. So bracing, action, and string gauge will still be the same if you capo up. Therefore the general tone of the instrument should still be more baritone than standard guitar.
The scale length of the bari at the 4th fret will probably be shorter than 25.5″ or even 24.9″. So there will be that difference too.
BTW, capo up to the 4th for E to E, capo up to the 5th for F to F.
I think about this stuff because I’m trying to find the perfect spot between mandolin and guitar. My 5 string emandos are 14.25″ and 15″ respectively. I’ve got a 17″ mandola and a 19″ octave mandolin.
When I capo the octave mando up to the 5th fret to catch the mandola tuning, I do mostly get the mandola tone. But this is probably because I use the same gauge strings for both instruments. The fretting is a bit tighter, but I’m comfortable with it.
In the end I’ll probably need to have someone build me a 5 string octave emando, GDAEB, at 19″.