In material terms, the province of Africa was the most important part of Justinian's conquests (at least theoretically speaking) since it had always been the granary of the West, Egypt being its eastern counterpart. Mainland Italy (Sicily was different, since its climate and natural conditions were actually more “African” than Italian) was, if not negligible, less productive. That being said, your question is indeed very intriguing, and a short answer could be: we don't really know. Administrative sources for the (Late) Roman Empire are, in general, very rare, and it is arguably even worst in the West than in the East -- it is therefore far from easy to quantify anything in this period. Furthermore, after Procopius (and maybe Agathias), the scope of Byzantine writers tended to become narrower and narrower, which means that Roman sources of the late 6th century practically tell us nothing of the newly conquered provinces (to the point that the short lived Byzantine reconquest of Spain is practically never mentioned, as far as I know, in Roman sources).

Therefore, assessments of the cost/benefit balance of these ventures are mostly guesswork. I would contend that the majority of historians would say that Justinian spent more in his moment of bravado than its successors would ever earn. They are influenced in this evaluation by Procopius, who criticises veyr harshly the financial prodigality of the emperor in his Secret History, and also comments on the damage caused by the conquest on the provinces. The last sentence of his Vandal War is self-explanatory: “Thus it came to pass that those Libyans who survived, few as they were and poor, at last and after great toil found some peace” (the influence that this kind of statement had in the historiography is, as a side note, a striking example of Procopius' extraordinary rhetorical cleverness). Similarly, the Gothic War is generally presented as a disaster, and it seems reasonably clear that Italy's urban civilisation, which was reasonably intact before (even though cities had already been declining), suffered a massive hit. When we compare this bleak picture with recent archaeological research that show that the Near East was blossoming, it is quite natural to think that the West must have been a drain rather than a source of income.

It is also clear that the neat mechanisms of Western trade and taxation had been gripped by the events of the 5th century, and could not be revived by an empire centred on the East. The prime example of that is the system that siphoned off African production towards Rome. After the loss of this province to the Vandals, this big incentive for productivity disappeared, and a century of Vandal rule was enough to guarantee the perennity of this change. However, we also know that by 600, Africa contributed to the supply of Constantinople. This simple fact shows that the province was productive enough not only to sustain itself, but also to secure a surplus. Similarly, the choice of Constans II to move to Sicily in the second half of the 7th century suggests that this part of Italy was wealthy (of course, obvious strategic considerations linked to the position of Sicily are the primary motive for this choice). We also happen to know, thanks to the Variae of Cassiodorus, that taxation survived during the Gothic period, and it is therefore beyond doubt that it continued to be exacted after the reconquest.

To summarise, I would say that these two provinces were undoubtedly less wealthy than before the reconquest (and the Germanic invasions), but that they were still able to provide for the expanses of their administration, and occasionally to contribute to the resources of the Empire. They were certainly not decisive, but they could be useful.

/e: the main sources for this post are my (vague) reading memories of Chris Wickham's Framing the early Middle Ages.