you might want to check first, to make sure that 4.0 wire will fit in the lug connections in your 200amp panel.
Also, 4.0 wire is VERY difficult to bend, especially in this cold weather. 150ft isn't really that far, as far as voltage-drop is concerned. (No offence intended, Bob)
If you are contracting this yourself, as a lot of homeowners are allowed to do, PLEASE make all your connections VERY TIGHT. There is tight, and there is VERY TIGHT, make them VERY TIGHT. Please pardon my shouting, but it's very important.
I recently was called to a very competent lady friend's home, which she remodeled & wired herself. There was an electrical burning smell coming from the 200amp panel. The 2.0 wire was burnt and black for 10" back from the NOT VERY TIGHT main lugs, and the insulation was all gone. I got there just in the nick of time.
Having said all that, I agree with Bob. If 4.0 fits, install it. If you ever need to up-grade your service, the wire is already there.