Your 1795 Dollar matches up as a BB-27, that means that it is either a well made die struck counterfeit or a perfectly legit coin, I am leaning towards the latter. I am fairly confident it would get a details grade though, because of the deep scratches and damage on both the obverse and reverse. I would like to see some of the other's opinions on these coins as well.
Here is a genuine 1795 B-5, BB-27 dollar. This piece has mint caused adjustment marks. I don't care for the reverse on the OP coin. It looks like a case counterfeit to me. I am not an expert of Trade Dollars. I will have to leave that one to others who know more than I.
If you were or are considering purchasing either piece, move on. If you have purchased one or both, you will be disappointed with the Grade, including the Grade of Genuine.
The Trade Dollar looks to have a die clash on the reverse. The obverse is quite ugly in my opinion. The last one is in my opinion beat up. I would pass m on both of these coins if you’re looking to purchase them.
I have written a Coin Week article on recent fake 1795 dollars of this variety; this one does NOT have the common matching attribution marks of the fakes. I have also documented a number of counterfeit "CC" Trades with several different common reverses; again, this one also doesn't match any fakes on file.
They both look OK to me on the authenticity front, though take that with the proverbial grain of salt, as I am no expert on either series. Both Trade dollars and early silver dollars are, of course, widely counterfeited, and require extreme caution. Both coins also have problems, and neither would straight-grade at a third-party service as a result, but they'd still be worth submitting for the sake of authentication and getting them into Genuine/"x-details" holders.
Thanks for the responses everyone! I got both at a great deal (even accounting for the damage). I plan on sending them off for grading in the not too distant future, so I'll update once results come in.