I won’t say that they look exactly like each other. But if you put the images next to each other, you can actually see the resemblance between the two. I think the resemblance has something to do with the hair and the nose.
People only noticed the resemblance between the two when Nikolaj Colster-Waldau (Jaime Lannister) said that his character in Season one of GOT resembled Prince Charming from Shrek.
In my opinion, I think it would also make sense if you compare Prince Charming with the likes of Obi Wan Kenobi from Star Wars. Prince Charming looks like a jedi master to me.
I think Prince Charming resembles Jamie more than Obi Wan due to the bone structure. Obi Wan has the hair, kind of, but his face looks softer. Jamie has the same hair and nose like you pointed out but I think his chin and bone structure looks similar too.
There are similarities with the face shape, but Prince Charming has a bigger face and body structure compare to Jamie Lannister. Their eyes is what gives me away with this comparison. Jamie and Prince Charming’s eye shapes are very different.
But ask yourself, what makes you happy?
For me, it’s in makeup, exploring past my boundaries, and doing something where I know I could be risking something
I don’t think many people would include themselves in the thread. That’s why I asked the question (anonymously) here. Because I don’t think many people have watched or watch GoT here.