Assessing the CR for a PC... huh?!

[Shin Okada]

You're thinking of 3.0e. Now he'd give +3, +3 and +3.

Oh, I seem to be too get used to using prayer bead Karma.

 

[Shin Okada]

Also, IME an NPC Barbarian is far more dangerous than an NPC Fighter. Just like with monsters, not all NPCs of the same CR are identically challenging.

Cheers, -- N

There is another thing better to consider. Somone who burn up daily reouces for combat (barbarian's rage, spellcasters spells and so on) are stronger as a one-shot opponent. Fighters are meant to be effective when there are many fights in a same day.