I wouldn't necessarily call it a competition, but there is a time when Morinaga's ex-boyfriend randomly showed up. Souichi told him not to see him again and freaked out when he spotted the two of them together after that. Seems like jealousy to me... Though Souichi wouldn't ever admit that, of course.
He hasn't ever said it, buuuut, he's hinted at it several times. You'd have to read it to understand, but you can just sort of tell through his actions and expressions that he definitely does love him. He's still too deeply a homophobe to admit it to himself much less Morinaga yet though. I have high hopes for the future!
So I haven't read it all, but can someone tell me in a spoiler if sempai ever says I love you or if there is ever a time where he has serious love competition of something similar to make him super frustrated over Morinaga?