There isn't really much of a difference in operation that I can see. It does seem that the 682 has more functionality on the digital side, like for trunking options. They both have the same or very similar IP rating. I have a 782 myself and its the best radio I have ever used. It would be unfair for me not to share what I have experienced. I have dropped it a few times on grass, pavement, concrete, gravel, even in a river. It's now 5 years old and still operates as it did when I first got it. I did notice that the 682 has a bigger band split option. 400-520 vs the standard 400-470/450-520. All of this is just my opinion.
Hytera PD682 vs PD782
The PD682G has additional options that are available due to the fact that the newest firmware is loaded onto the 682.
the PD782G when updated to the the most current firmware is on par with the 682. the T-Band Coverage of the PD682G is cool, but it's rare to find any usable spectrum for hams in the T-Band arena. I do prefer the PD682G over the PD782 due to its smaller size and it just fits so well in the hand. the PD782G has it's user base as well.those with big mitts for hands, ect.. The PD782G also has way louder RX audio than the PD6 series. and then there is battery life. it is much improved on the PD6 series. Both rigs are waterproof and literally bullet proof. I've had my PD782G for going on 5 years and it has taken so many tumbles and drops, I cant even count them all. still works famously. I love them both for different reasons, and wull carry the radio which best suits my task that day..