Published in Plos One, their study found empathetic people preferred more mellow, low-energy music.
While those who were "systemisers" - people who seek to analyse patterns in the world - enjoyed punk, heavy metal and more complex music overall.
Researchers say their work could have implications for the music industry.
Many people make snap decisions about the tunes they like or dislike, but scientists say what drives these preferences remains unclear.
To unpick this, researchers recruited 4,000 participants and put them through a series of different tests.
First, they were asked to complete self-reporting questionnaires with statements designed to assess whether they were "empathisers" or "systemisers" overall.
For example, people were asked whether they were interested in the design and construction of car engines and separately whether they were good at predicting how people were feeling.
Participants were then subjected to 50 short pieces of music spanning 26 different styles, and asked to give each a rating between one and 10.
People who scored highly on empathy were more likely to be drawn to R&B, soft rock and folk.
In contrast those who score more highly on systemising tended to like music by heavy metal bands and more complex, avant-garde jazz.
People who score highly on empathy might enjoy songs such as Hallelujah by Jeff Buckley and Come away with me by Norah Jones.
While people who identify as systemisers are encouraged to try Enter Sandman by Metallica.
And when researchers delved deeper, they found even within a given genre, there were differences in the intensity and style of music favoured by each group.
David Greenberg, a doctoral student at Cambridge University, suggests these findings could be employed by the music industry.
He said: "A lot of money is put into algorithms to choose what music you may want to listen to, for example on Spotify and Apple Music.
"By knowing an individual's thinking style, such services might in future be able to fine tune their music recommendations to an individual."

Northumbrian Water, which supplies water across the north-east of England, is expanding its cohort of water rangers.
It is recruiting new volunteers to walk by streams, becks, burns and bathing waters which are prone to pollution and report back on their condition.
The company's wastewater director, Richard Warneford, said the scheme had been "hugely successful"
"[It] has helped us to spot and deal with potential threats to the environment at the earliest possible opportunity on a number of occasions," he said.
New routes have been added in Northumberland, Tyneside, County Durham and Teesside.
The rangers are trained in environmental issues and what to look out for when monitoring watercourses.
The new routes are situated in:

The Baby Blacks - who won the tournament from 2008 to 2011 - ended England's two year hold on the trophy.
England went in front through Max Clark, who burst through, before New Zealand hit back through Vince Tavae-Aso to lead at half-time.
Akira Ioane went over from close range to extend their advantage, as Otere Black added four penalties.
England beat South Africa in the semi-finals, while New Zealand went through to the showpiece after thrashing France in the last-four.
The New Zealand juniors performed the haka before kick-off, but England started confidently, going ahead through Bath centre Clark.
After a slow start, New Zealand got back into the game as Tavae-Aso powered over for a narrow 11-10 half-time lead.
Ioane bundled himself over early in the second half, before being sent to the sin bin, and although Rory Jennings kicked four penalties for England, they relinquished their hold on the trophy.
A person's taste in music may offer insight into the way in which they think, researchers at Cambridge University say.
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A scheme to tackle water pollution is to be extended.
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New Zealand won the World Rugby U20 Championship for the fifth time after beating England 21-16 in Italy.