I believe God is in control of all things. I also believe He has put certain natural processes in motion that are natural laws because He made them that way.
For instance, it is a natural law that if you eat extra, you will gain weight. Now, there are some exceptions. Some people can eat more than normal and not gain weight because they have unusually fast metabolisms, but the general law remains.
Does anyone want to argue that I should eat and then pray that I will only gain weight if it's God's will? No, because we know how that natural process works. If I eat more than I burn, I will gain weight.
Now, I fully agree that children are a blessing from the Lord. I also know what needs to happen in order for a child to be conceived. The way natural law works, if the biological necessities are there, a child is going to be conceived. God sometimes intervenes to change natural law, but not often. If two people sleep together enough and are healthy, they will conceive. Are there exceptions? Sure, but the natural law is still there.
I don't see a fundamental difference. God allows natural processes to dictate how much I weigh based on how much I eat and burn (I realize that's a simplification). Does he care how much I eat? Sure, but the point is, He allows the natural process to work. In the same way, God cares very much how many children people have, but He allows natural processes to work in that area as well.
As long as a human being is not being killed by the birth control method used, I believe it is permissible. We no longer live in a time when half of our children die in infancy or when we need them to help us harvest crops. I believe big families are a great blessing and that we should be open to God calling us to bring more children into this world. I also believe that birth control is a blessing that allows us to change natural processes. If I eat, I'll gain weight. If I exercise, I'll be able to keep that natural process from happening. If a healthy couple sleeps together, they'll conceive. If they use birth control, they'll be able to modify that natural process and plan ahead.
All of that said, I don't wish to argue with someone who has a different conviction. People should do what they believe is right in God's sight.