The question of whether multiple Speed weapons can work simultaneously has come up many times, and always in the end comes down to "It's ambiguous; ask your DM."

But a strong little piece of evidence in favor of Speed weapons working together is often overlooked. In a relatively modern, well-edited splatbook (Magic Item Compendium), there's an item, the Quarterstaff of Battle, which has a special ability to temporarily give both ends of it the Speed property. That would be pretty useless if you couldn't use them both, methinks.