The Sendai-class had a significantly heavier broadside than a Fletcher, though with rate of fire and the significantly better metallurgy used to construct 5" Special Purpose Common shells compared to the Japanese 14cm Capped Common Mod 2 means that the Fletcher might actually outperform a Sendai in a gun duel. Which is hilarious and sad, since a Sendai displaces two and a half times as much as a Fletcher.
Can't be totally sure, since I can't find AP tables for the 14cm/50, but the Fletcher's 5/38 can punch through the 2.5" belt of a Sendai at about 10,000 yards, going by the table on Navweaps, and a bit of an educated guess.
Obviously, the Sendai has to simply hit the Fletcher, assuming Point Detonating HE is used, but 10,000 yards is an engagement range you could realistically see happening. And the Fletcher is pumping out anywhere between 75 and 110 rounds a minute from its 5/38s, versus the Sendai's 42 to 70 rounds a minute.
Fletcher: 6,069.8 lbs/minute maximum
Sendai: 5,866 lbs/minute maximum
Huh. Go Fletcher. Those numbers don't tell the whole story by any means, but they do show how little of a firepower advantage the Sendai has over the Fletcher, if she has one.
Any rate, this is a fight that probably favors the Sendai, since her size means she can probably take more hits, but it's a testament to just how good the Fletcher is that I'd buy the fight going either way.