It is pretty much impossible to know for sure, because, like you said, they didn't have comprehensive population surveys, and we have no records about most people's lives. In particular, we have almost no records of people who couldn't write, because they didn't write anything. So even if we have loads of records of people who did write, it's very hard to tell how many other people there were who we don't know about it. It's a sampling bias problem that's very hard to deal with.

But we do have some indications from both Jews and Christians that it was at least popularly perceived that Jews were much more likely to be literate. For example, one twelfth-century Christian writer said:

"When Christians send their sons to school, they do not send them for the love of God but for lucrative reasons [...] But a Jew, even if he is poor, even if he has 10 sons, will send them all to school, not in order to obtain any benefit, as Christians do, but for the study of the law of God, and not only the sons but also his daughters."

It's hard to tell how literally to take this text. Did he really know that many poor Jews with educated daughters? Maybe. Did he know that Jews care about education and then try to use that to motivate his Christian readers to care more about education? Also maybe.

We also have a number of Jewish legal texts saying that everybody ought to learn to read so they can read the Torah and rabbinic texts, and that all Jewish communities should appoint someone to teach the young children how to read. But we don't know how much anyone listened to those legal texts. We have a large number of financial documents written by Jews in Hebrew, many of them in non-professional handwriting, which suggest that at least merchants and their clients could read and write and didn't need to hire scribes for everything like many Christians did. But it is very hard to tell how far down that really went in socio-economic classes, and it is very likely that very poor Jews were less likely to be able to read.

Short answer:

There are all kinds of techniques for assessing the literacy of a historical population. There is, however, no "average medieval person" to compare Jews -- or anyone else-- to. The Middle Ages covers a great expanse of space and time, and literacy varies from place to place and from time to time in the nearly thousand years from the end of Antiquity to the Renaissance.

Discussion:

Obviously there weren't any kinds of census on reading ability,

Never underestimate the ingenuity of scholars in finding quantitative proxies. While there were no "censuses of reading ability" -- we have an enormous body of legal documents and financial, which often demonstrate whether a particular individual could sign his own name, a marker for the most basic literacy. This gives us a very nice time series for historical literacy, and can be further be broken down by gender and class (since early legal documents often mention individuals' occupations. So David Cressy (writing of early modern England, but the techniques can be applied wherever you have documents) is able to tell us, for example, that:

The social structure of illiteracy in the diocese of Norwich is clearly established by the study of depositions. Table I shows the percentage in various social categories who could not sign their names, and Table 2 shows the illiteracy of men in some of the most frequently encountered trades and crafts. Only the more common ranks and occupations have been included. Where samples are particularly small, of course, the figures should be treated with due caution. We may be 95 per cent confident that the true illiteracy of yeomen in East Anglia lay in the range 35 +/- 3 per cent but the illiteracy of, say, shoemakers should be more properly estimated as 58 +/- 11 per cent and bricklayers 88 +/- 13 per cent.

There's also an entire series of scholarly works, the Utrecht Studies in Medieval Literacy which attack the problem of evaluating medieval literacy in all sort of ingenious ways. And have to mention the important study by Buringh and Van Zanden [2009] -- they run the numbers on book and manuscript production from the 6th through the 18th centuries.

Some of the easily assessed proxies include the numbers of books published, and topics. Books often give you an idea of who it was intended for, no reason to produce a book for someone who couldn't read it. Its often noted that the transition from a medieval manuscript culture, where book production was small and expensive, to a printed book economy where they're plentiful and cheap implies a great deal more literacy. Care has to be taken in estimating earlier literacy- when paper and other materials were expensive, inexpensive and often overlooked media, like wax tablets, were often used. Just because we don’t have paper doesn’t mean people weren’t reading and writing - and some of these other media don’t survive well.

In terms of religious associations with literacy, Jewish males were commonly literate for religious purposes, but the more useful comparison is with Protestantism. Catholicism didn't require religious literacy for the people (it did for the clergy), and so the rise of literacy in Europe is often associated with both the printing press and Protestantism. But that's too simple as a story-- the role of the Church in education changes during the middle ages, and in later years there's very much an expectation that they'll be fostering education-- looking at England, literacy is increasing significantly even before the Reformation

As was stipulated in the canons of the fourth Lateran Council, cathedral schools were expected to extend their facilities to any youths who desired instruction in Latin. Although the cathedral clerks alone justified the maintaining of a grammar school, training in Latin was not to be restricted to them. This is frequently expressed in the appointments of the masters: when Bishop Welton appoints Master John of Burdon in 1362 to conduct a grammar school in Carlisle, he lays down no conditions for admission: instruction in Latin is open to 'boys, adults and any others' wishing to learn

So when you ask "were X more literate than average" -- well just where do you get your "average"? A slave in Wales in 900 CE? Then yes. Or a Florentine merchant in Paris in 1400? Probably not. "The average middle ages person" -- ain't a thing.

Sources:

Miner, John Nelson. “Schools and Literacy in Later Medieval England.” British Journal of Educational Studies, vol. 11, no. 1, 1962, pp. 16–27.

Kaeuper, Richard W. “Two Early Lists of Literates in England: 1334, 1373.” The English Historical Review, vol. 99, no. 391, 1984, pp. 363–369.

Cressy, David. “Levels of Illiteracy in England, 1530-1730.” The Historical Journal, vol. 20, no. 1, 1977, pp. 1–23

BROWN, MICHELLE P. “THE ROLE OF THE WAX TABLET IN MEDIEVAL LITERACY: A RECONSIDERATION IN LIGHT OF A RECENT FIND FROM YORK.” The British Library Journal, vol. 20, no. 1, 1994, pp. 1–16.

Buringh, Eltjo, and Jan Luiten Van Zanden. “Charting the ‘Rise of the West’: Manuscripts and Printed Books in Europe, a Long-Term Perspective from the Sixth through Eighteenth Centuries.” The Journal of Economic History, vol. 69, no. 2, 2009, pp. 409–445.