Sean,
If you want to contact me and provide your EXACT details of each I will be happy to explain them for you.
I’m a Realtor & Mortgage Broker and have helped dozens of Piggington readers.
Some of your closing costs are not going to change regardless of which loan you get.
It’s easy to get confused by the numbers.
$15,000 needed for a 3% down $200K loan doesn’t sound right.
Is the 3.75% an FHA loan ?
Is the 4.00% not FHA ?
with an FHA loan you may have mortgage insurance for 30 years. DO NOT assume that you will be able to refi to a lower rate and have it removed in the future as rates could be much higher and it may not make sense.
Without more info I do not know what you qualify for but 4.00% is not a great rate today if your mid credit score is above 740, even with 5% down.
Without EXACT information, NOBODY can answer your question and many suggestions offered here will attempt to be helpful but in reality be bad advice.