There is no difference Explanation: normally "implementing" would be a continuous action, so it means they aren't flipping a switch, the implementation is a process that they are going through over time. But, "start to" already means that something is a continuous process with a beginning, middle, and end. (By the way, it should be "Do you know when we start implementing "the" new feature"

The there no real difference in meaning. They are alternative ways of saying the same thing. Please note that you need the definite article "the" before "new feature" in both sentences. You can also say "we will start" instead of "we start" for both sentences, but the present tense is also ok.