There's no real direct evidence, but going by urbanisation (which is indicative of agricultural surplus, trade and specialisation), the Empire is very likely to have had a higher per capita income than early medieval Europe, though not higher than the later Middle Ages. The urbanisation shortcut may however overstate Roman prosperity as the Empire's geography, economy and institutions lent themselves to urban concentration (not least the substantial urban slave populations which sustained elite prosperity but may not have raised overall productivity) to a greater extent than those of the medieval west.

Who is ahead compared to say 1300 may depend on our areas: in a like-for like comparison of the western Empire's former European provinces I'd say it's the later period: comparing the Empire with the whole of late 13th-century western and central Europe it's harder to say, though my money would still be on the latter, partly because cities now had to earn their keep without the cushion of large-scale slavery and a Mediterranean empire of seaborne trade and tribute. The Empire was about sustaining Rome, then Italy, later a predominantly urban elite: the Middle Ages started out with no such orientation.

But the levels are broadly comparable: I'd extend that to Byzantium and the lands of Islam too. The key point here is that each of the four areas (or five, differentiating between Europe's early and late Middle Ages) relied mainly on agriculture (70-80% of the labour force outside Italy and comparable central areas, and perhaps something around 60% of current-price GDP), and there are bounds to what most of us can sensibly eat (or subsist on) and wear. Europe in the second half of the first millennium may well have been the poorest, but there too past perceptions of collapse and stagnation have come under review.