No, they are not identical in two ways:
1. #2 looks much better,
2. and the reason is:
it is a contemporary fake coin. It is manufactured in Dimitrovgrad or Haymanli, Bulgaria, where a series of workshops are specialized in making "museum copies", e.g. fake coins.
It seems a pity that you own #2

. I just hope you did not pay more than 3-5 USD for it!
Roman coinage is a mess on Numista, in addition to that, a significant amount of coin pictures show that
people actually own A LOT OF FAKE coins from Rome.
If in doubt, you can always check here:
http://www.forumancientcoins.com/fakes/index.php
a wonderful library of
11000+ ancient fakes. - with that Dr. Prokofyev is far away from covering the 50% of fakes of Roman coins
If you are into ROME, you need to be on the top, ... but it can be learnt .... probably the hard way (
and if you did that learning it turns profitable in many ways!
i.e. Did you know that Roman coinage has as many varieties as the entire World coinage from 1700-2000? It is a fascinating era!