Well, Hitsugaya has quite a lot of screen time, to be honest. Out of all the captains he's the one who has the most time shown. Moreso than even Byakuya. During the SS arc he's the one who conflicts with Gin and Aizen and figures everything out. While all the events with Ichigo are going on, he's the most center character involved in the captain's stories.
The death of Aizen, conflict of Hinamori, betray of Tousen and Gin, he was at the center of it all. Then when the arrancar start showing up, he's the one captain who's shown to be leading the advance squad. Hitsugaya gets plenty of screen time if you ask me. That's probably why he ranks second/third in most of the character popularity polls.
Shuuhei, hopefully, should get more screen time with the loss of his captain. He has a brief scene with Ukitake and a lot of people believe he'll suceed to the captain spot but he's shown little to nothing of his own skills in the series. Even against Yumichika, it flashes away and only comes back when the fight is nigh over. But he also seems to be a popular one among the lesser shinigami, so he'll probably be around more.
Hopefully, come this winter war, everyone will get their time to shine. So many captains/vice-captains who've yet to truly show off their skills. Here's hoping, right?
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