Two city-wide events on the same day?

Long story short: I am in charge of planning for a small city-wide festival to raise funds. Recently I learned that another organization chose to have their annual festival on the same day as the day for my event. This organization will most likely draw in the larger crowd due to the event's popularity. It is... show more Long story short: I am in charge of planning for a small city-wide festival to raise funds. Recently I learned that another organization chose to have their annual festival on the same day as the day for my event. This organization will most likely draw in the larger crowd due to the event's popularity. It is not possible to reschedule either event to another day.
Any ideas that will benefit both parties? Some ideas that have been thrown around are combining the two events, but none of the available venues will be large enough to hold expected crowds. Another idea was to set up a voucher system (pay for one event, get an admission discount for the other.) Any other ideas? All are appreciated. Thanks :)
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