Both are important.
A powerful processor will allow you to process data faster. This means faster app opening, faster web page loads, faster games, etc.
More RAM, on the other hand, lets your phone handle more tasks at once. This could be more tabs in a browser, multitasking, faster response from the phone apps and UI.
That said, almost all the phones in the market have enough processor capacity to give you the speed you need, the only downside is that a lot of them do not have enough RAM. So make sure you go for RAM not less than 1GB.
