One big difference is that artists pay to use a venue for a performance. Sports teams get the city to pay to build the stadium, and keep the profits.
When I go to the theatre or the symphony or the ballet or the opera, the programs and the placards in the lobby always make it clear that most of their funding comes from donations from big companies (in Seattle: always Boeing and Microsoft) and private donors.
If we're so excited to spend public money for gatherings at events that people want to see, why don't they ever spend that sort of money on the arts? Why don't I see Seattle Pops concerts on TV? Why do we depend on private donations to keep the theatres open? Why do we zone for stadiums, but not community theatre?
Everyone I know wants to see more of these performing artists but most have trouble affording tickets. When you can't afford an NFL ticket, you turn on the TV and watch it for free anyway. When you can't afford to see the local arts, you're mostly just SOL.