This is an important question based on the premise that interest rates are pretty universal.
lets evaluate your portfolio for a moment and see if this is really true.
Are you looking to refinance one property, or a portfolio of a few properties?
Is your property a single family or a multi?
If you have a number of single family homes or a multi-family building with 5 or more units you can refinance with a commercial loan. In the commercial lending world, rates are anything but universal.
A portfolio of SFRs can be refinanced with a blanket portfolio loan using a local bank or credit union.
These lenders often base their rates on different benchmarks and spreads which can get you varying results.
Just as an example, I got 2 different qoutes from banks this week on the same property. One qoute came in at 5.9% (yes i know prime is 7% today) the other came in at 6.75%. That is a difference of 85 BPS! (These lenders don't use prime as a benchmark. They aften use the treasury yield or SOFR and add 2% or 3% on top of that to come up with their rate)
In addition, Rate should not be the only factor in choosing your loan. Amortization is a big factor as well. If one lender will offer 20 year amortization at a lower rate, while the other might offer 30 year amortization at a higher rate, you might be better off with a higher rate amortized over 30 years, because it will increase your cash flow.
Recourse vs Non Recourse is another very important factor in choosing a loan. Many multi-family properties can qualify for Agency Non recourse loans. This means that if for whatever reason there is a default of the loan, the lender can only collect from assets owned by the LLC not the individual.
Also keep in mind prepay penalty. I just had a client that chose a higher rate to change his prepay penalty from yield maintenence to a step down prepay because that was a better choice for his exit strategy.
Lastly. when you are looking for a lender, look for someone that works for you. not for a bank. A good mortgage broker should look out for their clients and work with them to get them the best terms for their deal. Not just in the short term by selling you their rates, but in the long term by giving you knowledge.