The easy answer is to bring them both back. That would give the Chiefs a solid middle three to their offensive line, including center Rodney Hudson. Since Schwartz and Asamoah shared the right guard spot last season, the Chiefs could switch one (probably Schwartz) to the left side and move Jeff Allen to a backup spot.
The problem with this is that the Chiefs won't have unlimited funds to solve the problem. Schwartz and Asamoah will want to be starters next season and will want to be paid like a starter. So re-signing both players will require a financial commitment from the Chiefs that may not be in their best interests, particularly when they have Allen available to play one of those spots.
It's a tough call for the Chiefs. Asamoah will turn 26 this summer, Schwartz 28. Schwartz has the versatility to also play right tackle if that's what the Chiefs need him to do. As PFF notes, Schwartz is the better run blocker, Asamoah the superior pass protector. That would seem to give Asamoah the edge to Andy Reid and his pass-heavy offense.
Then again, the Chiefs opted for Schwartz over Asamoah last season. Asamoah began the season as the starter at right guard but missed a game in late November against San Diego because of a shoulder injury. Schwartz played so well the Chiefs kept him in the lineup for the rest of the season, leaving Asamoah on the bench. And don't forget that the offense began to make its move at the time Schwartz was put into the lineup, though it's difficult to make the direct connection between the events.
Either way, the Chiefs would be keeping a good player and a valuable offensive lineman. They would be losing one, too.