It was similar in certain significant ways: it was highly monetized, capital could be used to make profit, there was a lot of anonymous exchange, etc. But it also had many differences, driven in large part because the society and particularly politics of the empire were very different than today.

I did an AMA about this a while back that gets into a lot of the issues.

/u/Tiako does a characteristically good job navigating what historians sometimes call modernist and primitivist perspectives on the Roman economy. Modernists tend to see historical economies as being essentially similar to today's capitalist economy: monetized, capital being used to make profit, anonymous exchange, etc. Primitivists tend to focus on differences. For example, luxury goods often circulated as gifts, whether to gain prestige or loyalty – what scholars sometimes call "social capital" – but not to accrue debt or to trigger exchange. (It's kind of like the difference between buying that thing you want or behaving good so you can get it at Christmas.)

These models are both fundamentally based on comparisons with today's economy – Was the Roman economy alike or was it different? In The Roman Bazaar (2008), Danish historian Peter Bang recommends that we look to other models as well. He argues that the Roman economy worked more like the Mughal Empire of early modern India (1526-1857). There's good reasons for this. The Mughal Empire drew its income from tributes drawn from agricultural surplus, much like Rome, and not at all like modern capitalist states that depend on taxing trade. Ironically, much Roman trade was actually made possible by tribute, since the senatorial elite would smuggle trade goods on board the ships that carried tribute payments across the Mediterranean or redistributed them as food or final goods sent to military outposts across the Empire. So whereas many modern taxes would be impossible without trade, most Roman trade would have been impossible without tax.

Using the Mughal Empire as his baseline, Bang suggests that merchants had to operate in markets that were volatile and fragmented: exchange didn't drive the economy, so merchants had very little information about what their next shipment might be or what their customers might develop a need for. As such, they built personal relationships with other merchants – often through communal (e.g. guild), religious, or family relationships – much like we can read about in Rome. This fragmented the market further, and it certainly meant that merchants weren't maximizing profits like they might do in an ideal market of freely available information, but it gave them social networks that provided security in times of economic distress.

This isn't exactly the modernist perspective of free exchange. Nor is it a strictly primitivist perspective that all exchanges were actually made to achieve social ends. It's somewhere in the middle, and I think it's a very provocative suggestion.

Can I ask a related question? I often see it talked about how the Empire obtained grain, first from former Carthage and then from Egypt. But I don't think I see much discussion about how they got it. Was it a tribute? A tax? Did they purchase it?