Battles of Barbalissos and Edessa

[starman2012]

I think we can safely say that in this case the Romans were 'less enthusiastic' to report what occurred.

From what I've read e.g. in The Roman Eastern Frontier and the Persian Wars Barbalissos wasn't reported at all. The Naqs-i-Rustam/Bishapur account "finds no echo in Roman sources." At least one ancient writer mentioned Valerian being beaten in battle (at Edessa) but the apparent, official line was that he was taken by treachery.

The numbers may be accurate or not

I'd assume Barbalisssos involved the virtual eradication of Rome's eastern army. Extant Roman forces offered at least some resistance after Edessa.

(the captives helped build a city for the victors,

Dunno about a city but they did build a bridge and monuments including a big statue of Shapur.

But Shapur did raid Syria and conquered quite a number of cities, something he could not have done with a numerous Roman army still operating nearby.

Sure, that's good confirmation of their victory claims. They did get a little careless after Edessa though; Callistus and Odenathus counterattacked.

In this case, the Persians were probably more accurate.

I'd say undoubtedly. The Roman version is either lacking or propaganda.