This version of Shu appears similar to how his present counterpart appeared at the start of GT , having clearly aged since his last appearance in the original Dragon Ball series.
Future Shu's personality appears to be identical to the present Shu's.
Shu's life was exactly the same as his main timeline counterpart's until Age 767 when the world was put into ruin from the Androids. When Future Pilaf was about to using Dragon Balls to wish for youth, he expressed his worries about such a kind of wish as he heard rumors about monsters living in the nearby area. His worries were quickly filled when Pilaf's wish turned the whole Pilaf gang into toddlers. Unable to do anything more than baby babbling, he ran away together with rest of the gang, when Future Bulma and Future Gohan arrived, trying to save the last wish for averting the Androids' threat. After this, his further fate remains unknown, though he and Future Pilaf were certainly killed during Black and Future Zamasu' rampage on Earth and had their souls erased by Future Zeno.