I have been researching the denarii for these two and have not come to a conclusion. Perhaps those of you who have been collecting imperial Roman for far longer than I might want to weigh in.
It is surprising that no one has weighed in so far. I know that one of the experts here has avoided collecting these coins because he is leery of the circumstances concerning the striking of these coins. Given the Gordian I and II were emperors for only 21 days, it’s hard to figure out the logistics how word got to Rome concerning these men.
Remember, while it would take some time for word of the rebellion to reach the Senate, it would have taken just as long for news of their demise. The first step in any good imperial coup is to immediately establish the appearance of legitimacy by striking coins in the contender's name. There was no love lost between the Senate and Maximinus, and the Senate apparently wasted no time in propping up the Gordiani by striking coins in their names.
I have both in Sestertius format and can confirm from my research that at least in that denomination the coins of Gordian II are indeed even rarer rhan those of his father.
Probably 80% of the time I see them at auction, they are being sold as a set. When it's just a single coin, it's usually Gordian I, so I would say he is very slightly more common.
Somewhat rarer than Balbinus and Pupienus. I have the latter two in sestertii but am actively looking for Gordian I and II so I will have a coin of each of the six emperors of 238, which are Maximinus, Gordian I and II, Balbinus and Pupienus, and Gordian III.
Denarii I cannot advise on since my only Roman are large bronze -- sestertii and medallions. But for sestertii, though both are considered to be of equal scarcity and comparable price, I have found Gordian2 to be *MUCH* more elusive than Gordian1.
....from where i'm sitting, both are virtually non existant and unattainable...so it'd be better for me to try to figure out how many angels would fit on the head of a pin...
A while back I missed out on a great opportunity to add a beautiful denarius of Gordian I to my collection. It still stings. Purely anecdotal, I found it much easier to find Gordian II.
Here is some data on relative quantity: Banti in I Grandi Bronzi Imperiali (1987) found the following numbers in museums and collections: Gordian I: 131 Sestertii Gordian II: 103 Sestertii Rasiel Suarez in ERIC II (2010) lists the followig numbers offered in public sales in the internet age: Gordian I: 36 Denarii, 33 Sestertii Gordian II: 45 Denarii, 15 Sestertii OCRE inludes in it´s sample of museum pieces: Gordian I: 14 Denarii, 30 Sestertii Gordian II: 10 Denarii, 9 Sestertii Therefore while there may have been an equal amount of Denarii struck for both, it seems certain that there were less Sestertii produced for Gordian II.