I didn't catch the acres amounts between your "Big" property and your neighbors property that borders the 40 ?
Anything that a lot of the deer studies have shown us about "growing" mature whitetails is that it takes a lot of CONTINOUS acres to do it. If your neighbors are truly beating you, and they truly are passing bucks under 140", who cares ?! Unless there is a 10' wall that separates your properties, then you are reaping the benefits of TOTAL acres under strict management. The more the merrier.
I wouldn't mind owning 40 acres (or even 10) that butts up to a "big" property as long as it was managed with similar goals. You get the benefit of piggy backing a large number of acres under strict management and don't have the financial burden of owning the lions share of the land. Gotta have those continuous acres to grow them one way or another
I definitely wouldn't treat that 40 like a "inferior property" if the total acres WITH the neighbors reaches totals that studies show can successfully be managed. If the totals are close, and your goals are a 150", and the neighbors are passing <140" that might even be a better situation to reach your individual harvest goal.
If they are hunting their property at all, I'm sure the deer are feeling some pressure....just have less than that, and that might be all it takes to find the oldest buck in the area.
What are the totals of management acres if you compared the 2 situations?