It is better to under-promise,

that to fall short of promises.

The first will impact the impression of your capability but the second will affect the impression of your integrity.

Over-promising can be a good way to start things off, but if promises are not kept, regardless of what you deliver, you will not be able to sustain. People will not come back to you.

So, promise less - and outdo that promise. Slow and steady wins the race :)