Bright Local uses the zip code center, and Local Falcon uses the location's exact geo-coordinate as the center of the grid. If the business is located near the zip code center, then the results will match up well. But if the business is located at the edge of a zip code, and there is some distance between the two, then Local Falcon will have a different, more exact result.
Both tools are returning accurate results, but they are checking the results from different locations.
For example, this is zip code 30606. Its center is the black dot which I have added.
Using Local Falcon, you can pinpoint the exact location that Google says is the center of the zip code as well by just entering the zip code btw.
If a business is at the edge of the zip code, it will be a few miles away from the actual center in this example, which is where Bright Local is scanning from. If there are many businesses with the same category in that space, then the results will be less accurate.
Local Falcon, and the other geo-location rank checkers are more accurate since they scan from the actual location of the business.
Here's an overview of the lawyer offices in zip code 30606
This is Bright Local's results from it's free scanner for 30606
..makes sense as Jeff Field & Associates is the closest to the center mark (plus seems to have a strong listing)
You'll see that with Local Falcon, we have the same result of the #1 ranking in that spot for that business.
In fact, if you click on the Ranking Pin which is almost exactly the zip center point to get the detail popup in LF, you will see this:
which matches exactly what BL results are.
However, Thomas A Camp which is still in the zip of 30606 (at the lower left edge of the zip code) would see a much poorer ranking from BL (The 2nd page of BL maps result never works for me as it does not keep the zip code intact so I can't screenshot) Someone else can check and add possibly.
But with LF, you will see a much clearer picture of why BL and LF would give different results.
Local Falcon ignores zip codes, because checking by zip code center has no actual meaning to ranking. Proximity to the business does.
Sometimes Local Falcon will glitch because an address is not standard for example, or the API hiccups for some rare reason, so if you see a large discrepancy between Bright Local and Local Falcon, probably BL is more accurate. But if you see small differences of rank order placement, it's because BL is scanning from a point that is further away from the business location.
