While all cities show signs of healthy mortgage competition nationwide, some areas have higher concentrations of lender activity but also face varying degrees of competitiveness based on loan type, according to LendingTree.

As home prices and average mortgage rates continue rising, homebuyers are more prone to shop around for the best possible deals. And because the mortgage market varies geographically, lenders should pay attention to how the competition stacks up in their particular region of business.

Overall, competition is greatest in cities with the lowest amount of market share concentration.

Lender activity varies in intensity depending on how in demand a specific housing market is. In areas where lenders are originating the most loans, homebuyers could actually be getting some of the best deals rate-wise as lenders explore ways to entice borrowers.

The most competitive conventional mortgage markets were Providence, R.I., Boston and Hartford., Conn., as market share for the top 10 lenders was under 40% for these cities.

Comparatively, some of the most costly markets have the least competition among lenders for conventional loans.

Expensive real estate markets like New York, San Francisco and San Jose, Calif., were all in the bottom 10 for conventional loan competition, as the top 10 lender market share was close to or above 50% in these areas.

But, areas that are less competitive for conventional loans are more competitive for Federal Housing Administration-insured loans, suggesting lenders in these cities may be concentrating on that business. On average, FHA markets are more competitive than conventional markets. Meanwhile, the markets for Department of Veterans Affairs-guaranteed loans are less competitive than conventional.

Potential savings through comparison shopping can save homebuyers nearly 10% of their loan amount.

The competition data is derived from LendingTree's Herfindahl-Hirschman Index, which uses a formula based on Home Mortgage Disclosure Act data to measure how competitive a market is. The index creates a score ranging from near zero to 10,000, where a lower number represents less market concentration and thus greater lender competition.

The highest HHI across all loan types was 521. For context, "The Department of Justice considers a market moderately concentrated when the HHI is above 1,500, so values below this are viewed favorably," according to LendingTree

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