I use two sports apps for the most part. The Score and Sports Alerts. For sports scores, The Score is better organized. they have one page with all the day's games and scores on that page. - you can favorite your favorite teams and they will all appear at the top of the page that shows all the scores of all your leagues. The Score has recently added live activities feature for most leagues they support.
That being said, Sports Alerts does a better job with it's live activities feature as far as the detail is concerned. They have live activities for the NHL, MLB, NFL and college football and basketball (there may be others, I just don't follow others) but each sport gets its own tab. So you have to tap on the league tab to get to the sport and game you want to start a live activity for. Sports Alerts has better detail in the live activity that you see on your screen. But maybe The Score will get better over time.