They are similiar in many respects. For "cool factor", the 645 was the pistol used by Sonny Crockett, in seasons 3 & 4 of Miami Vice.
The trigger guard of the 4506 is rounded, which lends it more to holster usage. The 4506 is also newer, and more were manufactured, in the 11 years they were in production, VS the 3.5 years the 645 was made. So you're liable to find the 4506 has less wear, and is a better shooter, whereas the 645 is older and rarer.
Let me preface this by saying I am a revolver kind of fellow. I know enough about self loaders to tell from which end the bullet emerges. I had a 645, I found it heavy. I also found the magazine well a bit long and that created a long reach for the trigger. (I do not have a small hand and use an N frame for EDC.). The sight were fixed and adequate. As much as I tried to like the self loader ( any self loader) it just did not happen so it went down the road.
So, take my advice with a grain of salt as self loaders and I are not friends.