Generics of anything are not necessarily less or more effective than brand names.
Everyone's body chemistry is different, and how bioavailable the drug becomes in the body is different from patient to patient. Generic medications have to have an average bioavailability match of 80% to get approved... but that's not to say that for YOU in particular, the generic doesn't have more while the brand might have less bioavailability in your body. It's something you'll never really know from routinely taking a medication.
So, for some people, a generic of any type of medication may work better than the brand. The only difference is the company making it, which means they're probably using different inactive ingredients like colors and compounds that hold the tablet together, and the fact that the generic company doesn't have to pay off the costs of research.
So, I'm sure the generic will do just fine for you. Use a backup form of birth control for 3 weeks just to be on the safe side to give your body one cycle to adjust to the change, (not a fault of using a generic but of changing your medication). Then you should be fine.
Here's a tip though, somewhat unrelated to your question: No birth control pill is 100%. My cousin just had twins while faithfully taking her pill after she had a daughter a year ago who was conceived while taking a different pill. SO, if you are absolutely not ready for a baby, it's not really worth the risk on or off the pill, you should use back up anyway.