It's not really a good comparison. Or, it depends what you are comparing.

If you're not familiar, basic Roman education ( I'm talking Roman Empire, and in my case let's go with circa 4th century AD because that's the example I'm going to use later), had these tiers

1. Initial education, either privately or in small schools, focused on fundamental literacy, memory work, dictation, etc..
2. Grammar: (from age 9/12 - 14/15) involved reading, memorising, recital, and analysis of literature.
3. Rhetoric: from 14/15 onwards, a boy might study rhetoric with a private tutor, or in a small school setting. This would involve obviouly a focus on public speaking, but also argument analysis, and a broader 'humanities' set of subjects (continued literary work, philosophy, possibly music and geography)

Remember, this is restricted to social elites, and stage 3 as much less common than stage 2. You can think of stage 3 as something like high school.

Further study did exist, and it was usually either (a) Philosophy, usually undertaken in Greece (Athens, for instance), or (b) specialised legal studies.

Now, this produced incredibly well-trained Humanities-type scholars. My go-to example for today is Gregory of Nazianzus. Born ca. 330, grew up in Diocaesarea, a small town in western Cappadocia, his family part of the provincial elites.

His education involved private training by Carterius, before gramming and rhetoric staring around 345/346 in Caesarea, they then moved to Caesarea Maritima in Palestine, which was almost a Chrisitain-univrsity town. In 348, Gregory moved to Alexandria, and then to Athens, where he spent almost a decade studying rhetoric and philosophy.

Now, Gregory is not a representative example in terms of the average, but of the elite. Apart from biblical texts, Gregory Nazianzen was the most copied author in the Byzantine empire. His oratory, and his command of philosophy, are top-tier.

How does this compare to our educational system? Keeping in mind that we don't undergo the same types of training exactly, this is PhD level stuff.

So, to circle around to "are the skill levels about the same?" then yes, there's no deficit in intellectual ability or attainability. But, and it's a big caveat, Greco-Roman education was tightly focused on what we think of as the humanities, and other 'fields' were extensions of that. There are no 'scientists' (by a modern definition) in the ancient world, the scientific method doesn't exist. There's no school for civic engineers, etc..

I hope this has gone some way to answering your question or at least giving an insight into late antique education.