Regarding the specific questions about your website, it is up to you to decide which payment methods to accept. If you want to accept small payments, Paypal and credit cards may not interest you because of their high fees. So both Flattr and Bitcoins can replace Paypal as an alternative for cheaper micro-payments.
As for advantages/disadvantages:
- Flatter charges 10% of your income
- Bitcoins are not limited to small payments (you can accept any amount of them without fees)
- Bitcoin price fluctuates a lot right now - you might want to consider using bit-pay if you want a steady income.
Like other answers stated, you must understand that these are different systems. One is a currency and the other is a service. They can complement each other and you don't loose anything by accepting both.