"Better rates..." Depends on context. Is this a Conforming Conventional? Most small brokers can beat everyone out there, but do they know new construction? Can they prove this, not just "say they know new home lending"?
If your loan is higher than a standard conforming loan and you have additional cash to spare beyond your down and closing costs, Banks will beat anyone.... But also, does your loan officer know new construction? Can they prove it, not just "say they know new home lending"?
The builders lender is often able to match legitimate offers.... Once you are able to lock. If your new home is 90-120 days out, shopping for a loan at this point is if zero use to you. Example: Company A says they can give you a 5% rate today compared to everyone else's 5.25 rate...but that price is only for a 45 day lock. If you lock, can you float down? Is it in writing from the company (not the loan officer). Company A might be competitive today, but how about in 90 days?
All in all the best time to shop for rates is 60 days prior close, and get it all in writing from at least 3 lenders. If you can't get a rate quote in writing from a lender without a credit run, it's not a company you want to work with.
Bear in mind that a better rate is only better if it can be delivered on both you and your builders requirements. Everything else is just an empty promise, one that you can't risk your financial future with.
Best wishes for success with this task.