In this case it is quite obvious that the verse in Chronicles is the original text. The text as is preserved in Chronicles reads smoothly: Jashobeam, the Hakmonite (literally: son of Hakmoni) is a chief officer for David and killed 300 people with his spear. The text in Samuel however is badly corroded and fragmented that it is barely readable. This is a literal translation of the original text:
These are the names of David’s mighty warriors: Sits in
Shebet-Takhmonite. The head of three--he is Adino the Eznite [...] against
eight hundred men, whom he killed in one encounter.
As you can see the text doesn't read at all. Who is sitting in Shebet-Takhmonite? Did a town by this name even exist in biblical times? It is not found anywhere else in the bible! Furthermore, shouldn't the text name the warrior before mentioning his hometown? And the phrase "head of three", seems to be misplaced as well, since the text hasn't yet made clear that three warriors existed (See verse 18 for example, where "head of three" makes more sense as it follows after the three warriors have been mentioned. This is probably also what caused some scribes to correct the word שלישים to שלשי resulting in yet another scribal error). Then the words עורר את חניתו (raised his spear) are also missing from the text, and we are left to fill in the gaps "[he raised his spear] against three hundred men, whom he killed in one encounter."
As I have noted in the comments, the NIV completely disregards the words Adino the Eznite and exchanges it with "raised his spear"; so they have already played around with the original text, but the original text does not contain these words. Indeed the NJPS translation has the words "he wielded his spear" in brackets (after "Adino the Eznite") to show that it is not in the original text. Some translators have also noted the problematic words יושב בשבת תחכמני in the beginning of the verse, so they have chosen to reinterpret it as the name of a person called "Josheb-basshebeth". The NJPS has taken this regrettable route, but this translation is of course ludicrous, as the word יושב is a known and common biblical word which refers to "sitting". And adding confusion to this, this supposed Josheb-basshebeth would somehow have to be synonymous with Adino the Eznite though they don't bear any resemblance, and seem to be completely different people! The reality is inescapable, that the text in Samuel is fragmented and unreadable.
The text in Chronicles however follows the natural order and reads smoothly: first it names the officer Jashobeam, the Hakmonite, and then it goes to tell the mighty deeds that he has done. So ultimately we have to favor the text in Chronicles.
The only anomaly that remains is how the words עדינו העצני = Adino the Eznite made it into the text in Samuel. Is it merely a corruption of עורר את חניתו? it is hard to see how it became that. Is it perhaps the name of a different warrior which followed after Jashobeam the Hakmonite in the original text but later became one with the Takhmonite? But then we would have to explain why this name is missing from Chronicles? This question must remain unresolved.