Generally, improvements in brightness have come about a result in improvements in manufacturing processes and materials. The electrical characteristics of the brighter LEDs don’t differ drastically from the older generation of indicator LEDs. In a lot of cases, the brighter LED is just more tightly focused.
In almost every case, replacing an indicator LED with a brighter one is a simple, drop-in replacement. You won’t need to consider the electrical characteristics other than to make sure the polarity is correct. There are exceptions, however, and they can be tricky—I’ve had problems with floppy drives with replacement LEDs. They appear to function normally, but won’t read disks properly. Computer cases have LEDs for power and hard drive and possibly other functions—these can be swapped out with no problems.