“Βέβαια” and “βεβαίως” have exactly the same meaning (certainly, of course). “Βεβαίως” has an older suffix (-ως) while “βέβαια” has a modern suffix (-α). Both forms of the word are correct and are used in modern Greek. However if someone speaks or writes more formally, he would probably use the form “βεβαίως”.
-Θα έρθετε στο σπίτι; (Will you come to the house?)
-Θα έρθετε στο σπίτι;