Dweezil's SG is not Frank's. Its a custom made SG, stock straight from the factory. Its a very nice guitar with some incredible tone.
As for Dweezil, check him out, you will not be disappointed. His playing is very different from Franks but Dweezil actually took 2 years off from day to day touring and everything to study Frank's music. His guitar playing has really taken off. He is an amazing soloist right now. No one can play like Frank but Dweezil is certainly doing his dad justice. Dweezil's journey and what he is not only attempting, but actually pulling off, is truly awe inspiring. I have seen Dweezil get choked up and cry during solos, he reveres his father and his fathers music and does it justice to say the least.
I cannot imagine living in that kind of shadow and yet he is embracing it and he has assembled one of the best bands I have ever seen in my life. Every one of them is an amazing musician. If you ever get the chance to meet him he is one of the nicest people around!