An often discussed topic with my clients (and my colleagues clients). I want to address this.
Everyone wants a deal. Buying a home is a huge investment and having a payment that fits your budget is essential. No one wants to be house poor.
So then, you should shop around and get the very lowest payment possible right? Well that depends...
The old saying "You get what you pay for" does still exist. Even in the mortgage business.

First of all, no legitimate lenders should have huge differences in costs.
Rule #1:It costs a bank "x" amount to loan money and they to have to make "x" (reasonable) profit.
The monthly payment does not tell the whole story! Don't be fooled. Many lenders will try to show you a great monthly payment but will have either a loan origination fee or will have you "buy points". This money is due up front at closing. What's the difference?
Loan Origination Fee (PROFIT). Again Rule #1 applies. They are saving you $25 a month - but is it a net savings?
Paying for points: A fee paid at closing to "buy down" your interest rate. Example: $300,000 loan; 1 pt = 1% = $3000. Lowering your Interest rate from 6.875 to 6.75 (discount amount varies). Note: Points ARE tax deductible.
So how to compare? Should you pay points? (You should never have to pay an origination fee unless you have some credit dings).
Here is an example to calculate:
Lets say Lender A quotes you a monthly payment of $2000 with no points. Lender B is charging you 1 pt ($3000) but your monthly payment is $1975.
Over 30 years that a savings of $9000 - but who lives in a home for 30 years?
$3000/25 =120 months or 10 years. You need to live in that home for 10 years for this to be a good deal. (Now this is not EXACT; as there is some difference in how much you are paying to principle, etc.; but you get the idea.)
You must also consider service. Use a reputable lender. PERIOD. They should have a local office and hopefully you have heard of them before (and not via a TV or Internet Ad).
If they can't quickly call you back from day 1 or give you an estimate in writing (called a Good Faith Estimate or GFE); consider if that loan officer will get the loan closed on time? Do you want to save $10 a month and risk not even getting the house or know you will get the home you want without penalties or major headaches.
Lastly; as I have said before - ALWAYS compare similar loan programs from different lenders and ask your accountant, attorney and/or Real Estate agent to review them if you have questions.
Why do you perceive a relationship between origination fees and credit scores? I do not understand that.