You didn't mention the amp rating of your possible replacement battery. Is it also a 20 amper? That information could be a deciding factor in your new battery purchase.
Your battery powers the bike's ignition, lights and any accessories you may have powered up. The alternator and related equipment simply keeps the battery at peak performance based on the load you are asking the battery to handle. Some folks opt for more alternator output due to their running twin headlights on high beam, running lights, a DVD player, cappuccino machine, heated seat and grips, blah blah blah.
If your electrical load demand is modest, you may be OK with as little as a 16 amp/hour battery. Remember that the starter is a big electrical drain even before the engine kicks off.