The larger bat stick may have a longer travel distance... however, you also have greater leverage and ability due to your entire hands reaction.
The Thumb is actually a pretty slow digit. Try moving your thumb left to right back and forth repeatedly for 20 seconds or more. Then do the same with your fist rocking as if holding a stick. Less fatigue, and faster more precise responses.
The only exceptions, would be if you are using a very crappy cheap-o stick. Most people will rightly so use Happs Competition sticks for most general games... Dedicated Leafs for classics, and some use the tighter less-travel Japanese sticks for shumps and other games.
Each stick has a certain advantage / disadvantage... but overall, they should be miles better than a gamepad.
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