They are not real. The details are wrong the denticles are wrong and the lack of detail is not from a weak strike and wear. They’re bogus
If you make him pay for authentication/grading, I see no reason why to not do so. Keep in mind that everyone here is looking at pictures of cleaned coins in poor lighting. That is going to make the coins look odd and distort the details. If you could take better pictures of the coins one at a time (on a black background and with at least two light sources), you might get different answers. My first thought from the pictures was fake, but closer inspection revealed that if fake, they are some of the better ones I have seen. One thing I notice is that the high points have a different color than the rest of the coin. That signifies circulation wear and is extremely hard to fake. Where the designs are not worn, the details are very sharp and look like what I’d expect from genuine coins. Fakes from China, in my experience, do not have this quality. The anomalies with the rims can be explained by rim bumps. As for the edge, your picture is too blurry to tell. I had one in FR/AG condition, and the edge markings were surprisingly sharp. One quick test is to try to stand the coin on its edge. Most fakes are struck within a collar, so the edge would be flat, so it would stand up on its edge. Genuine coins were not struck with a collar, so the edge is a little rounded, meaning the coin will not stand on its edge no matter how hard you try. Could these be expert die-transfer copies? Maybe. But they are not your normal cheap fakes. That is why I recommended sending them in.
Now with my foot in my mouth (and looking at a screen bigger than my phone), here are some issues I see that make me question authenticity: First things first, the left 1803 coin is a half dollar. There seems to be a little die break in the 0. Cursory glance into the varieties for this year says that does not exist. On the 1803 dollar, there is a major die clash on the obverse. Again, a cursory glance through the known varieties suggest this never happened. Aslo, if it was on the high points, whould it not have gotten worn away first? Perplexing. On the reverse, there seem to be toolmarks in the rim below the eagle. The rim on the obverse appears to have a lip, suggesting a possible collar strike. The obverse on the 1798 seems to have toolmarks to the left of the date, and the dentils around the obverse, particularly below the date, look quite odd.
I would pass if it were me. The details look a bit mushy, and the color just seems "off". I would only buy coins of this series only if they are graded by one of the major grading services. Though authentic raw ones can still be found, you will save yourself a lot of second guessing and headache buying slabbed. As someone mentioned, these coins are not cheap, with problem free coins even in vg 8 or so going for around $1000. Though the date is different, check out my avatar of my 1800 10 arrow reverse, purchased from Heritage in January 2013. This will give you an idea of what an authentic heraldic eagle dollar looks like.
They both posted today on ANACS as legit. Looks like many of us were incorrect on them. Should have them back soon! Glad I only listen 99% of the time!
Good for you, but why you included my post in with the others I do not know, especially considering the fact you didn't bother to address what was said. In no way, shape, or form did I say one or the other was fake or real, and had you cared to look you would have seen the link I posted just happened to be a match for the one. The entire point was made with the hopes of getting you to not "listen" to the opinions of others that may or may not have the faintest idea of what they're talking about (hint, hint).
You were the only one that was correct so I wanted you to be notified of the results in case you were no longer following this thread. I appreciate your input on this one!
Oh, well thank you. If such coins are your area of interest, and if you're not familiar with the linked site, it's really an excellent reference worth exploring as well as bookmarking even if it doesn't prove a match automatically authentic. That said, again congrats on things working out in your favor.