1940s Bullseye - Need help from experienced eyes

Hi guys , new to the forum so sincerest apologies if I am posting this out of turn or even somewhere where it's not supposed to be posted.

I need help and opinions on a vintage watch I'd like to purchase for my grandfather on his birthday.

It is an omega bullseye that shares the same year as birth as him and fits in perfectly with his love with anything vintage/vintage looking.

On the left is the picture of a bullseye dial and movement from a renowned and trusted vintage omega seller, on the right is the image from a private seller. I am not purchasing from the renowned seller primarily because of price.

I've tried comparing it to the best of my abilities and find that the movements match up exactly, part for part (please do correct me if I am mistaken)

I am not sure about the dial however. I cant find a mint picture of the exact dial to compare its hands...which is the only thing i really know to look out for for this model.

Any advice will be much appreciated , thank you so much !

FYI There is also one for sale at the moment in the private sale section.

Hands look bad,, running slow so regulator pushed over and fingerprints on the movement. Not taken care of

May i know how you assessed the movement as "looking tired"? I would love to understand how you are able to pick that up

I believe this is what you are referring to as the regulator correct? Is it something that can be fixed/tuned easily?