Laminar flow and turbulent flow are not directly linked to Reynolds number, even though Reynolds number is a heuristic indicator of when the flow may transition from laminar to turbulent. However, the transition is actually not well-understood and is difficult to model/predict. That's why you will see cases where, for the same Reynolds number, one flow is laminar and another is turbulent.
Let's take a flat plate for an example. The flat plate boundary layer in laminar flow actually has a closed-form solution; the skin friction drag is given by:
As you can see, as Reynolds number increases, the drag coefficient decreases.
Turbulent flow, on the other hand, has no closed-form solution. An approximation for a smooth plate is given by:
The two lines are plotted in the figure below (cited from this Penn State course, which has a pretty good summary of boundary layer results for flat plate). As you can see, at the same Re, laminar flow has less skin friction drag than the turbulent counterpart.
From a skin friction drag perspective, if you can keep the wing in laminar flow, then all the power to you. In practice, however, this is very difficult. Any un-eveness on the wing (e.g. rivets, steps and gaps) could transition it to turbulent flow downstream. Any contamination, such as insects, could potentially ruin it.
Another consideration is whether staying laminar for the whole wing is desirable from a flow separation perspective, since laminar flow separates easier than turbulent flow. There will be a trade-off amongst stall speed, high AOA handling and drag.