I would go with the newer 7750. It is built on a newer process hence it will run cooler, therefore should actually last longer as well. This would be a big factor too since you will be running it 24/7. Plus it will run quieter.
By the way the 7750 and 550ti are much closer than you think:http://www.tomshardware.com/reviews/radeon-hd-7770-7750-benchmark,3135-6.html
Personally...I would be kind of pissed if I walked into a gaming kiosk and found out it can play most games at 1920x1080 at around 30FPS...I would expect to at least see 40-60FPS in most games - if I had to pay for it.
Edit: You could even get a passively cooled 7750 to eliminate noise:
SAPPHIRE Ultimate Radeon HD 7750http://www.newegg.com/Product/Product.aspx?Item=N82E16814102980