Many people tie their boats to a dock overnight. You must take into consideration the load the line can handle. New or old, if the load of the line is not enough, it will break under rough conditions.I have found that when it comes to line smaller is better. disclaimer: if we are talking about brand new lines I think the smaller of the 2 would be more then fine.
The reason I like smaller lines is because it allows you to wrap more line around the cleet. Both dock side and boat side. With the wider line your not able to get as many hitches or loops around what your tieing to. Also the size of the cleet on the dock and your boat dictate what size line gives you the best holding situation. No use going bigger on a small to medium sized cleet like what our boats have
On a related/unrelated story about thicker line:
I bought some new anchors and I went for the "mondo" anchor line. Yea it looks cool but it's no better for simple day use and total overkill to the point that I got some new thinner anchor rope. Much easier to deal with for day to day use. Doesn't soak up 1/2 the water that ends up back I the boat when you pull the anchor back in.
Also another tip. Stay away from colored anchor line. I got black and it's harder to see your line. "White is Right" it's nice to look out and see your bright white anchor line and how it's doing much Easyer then a dark black line.