Couple of things to consider.
Generally in these strips it's the same 5050 LED modules, but in the 5v strip they are all in parallel, in the 12v strip they will be in sets of 3 in series and then parallel between all the sets. This is because each module needs around 3.2v - the rest is dropped across the current limit resistors and lost as heat. On 5v about 1/3 of the power is lost in that heat, for 12v about 1/5.
So if you replace 5v with 12v I wouldn't expect much change in brightness but the big change is you will only be able to cut the strip every 3 LEDs on 12v not every LED as on 5v. That might be important if you've trimmed the strip to a specific length that doesn't divide by 3.