The pros and cons are the same for most engines.
Pros:
You get a nice power gain.
You can adjust compression ratio, piston rings, piston design and rod ratio while you're in there although stock is not that bad so there's not as much gain to be made compared to an older engine.
Cons:
It costs a lot.
You have to bore and hone your engine.
You should upgrade the cam to meet the new amount of air the engine needs.
If you go too far you can have the pistons unsported at BDC.
You get more block flex.
You can have issues with pin location on the piston.
Rod ratio can be a problem.
Block may need clearancing
All the cons can be an issue but if you buy a 408ci kit you shouldn't have much hassle with it as that is a common stroker kit size. Strat going over 427ci and you'll start running into issues. I think L77 is about 365ci stock from memory.
Edit: also you'll want to get some new heads or send yours off to Higgins Race Heads for a CNC port job. This is because you'll be flowing more air. LS3 intake is all you need in that area. And obviously the stock headders will be a bottle neck too.