I believe you might have a typo. One of the tubings is 0.004ID not 0.0004ID, is this correct? In any case the smaller ID tubing will giver sharper peak shapes because there will be less band broadening due to the lower volume. Noise is a non-factor in this case. You will notice an increase in pressure. If you plan on using the same ID tubing to connect in series to a MS detector after a UV detector, you must be wary of how much 0.0025in ID tubing you use to the MS detector. It can increase the pressure significantly if the tubing used is too long. This in turn may pop a leak, break a flow cell, or break a MS capillary if the backpressure is too high of an increase. Before you explore tubings post column, observe and note the pressure in the console before you attach a new tubing ID and after to determine the delta presssure. If you are performing method development, this information can be crucial when changing solvent conditions and appropriate flow rates.
Hope this was helpful!