The latest National Student Survey (NSS) stats suggest that employment outcomes 15 months after graduation, for history grads, are very similar for both unis, with c. 35% going straight into grad-level employment and c.20% doing further full time study. Some people dismiss the NSS but so long as you look at results with reasonable sample sizes, it can give a good general steer.
York has a marginally higher proportion, of those in grad-level jobs, going into the finance or business sector. However, be aware that York will probably draw a higher proportion of SE-domiciled students who may have easier access to London-based jobs by virtue of having a home base there after graduation. All this says to me that Sheffield holds its own relative to York in relation to employability.
Others may post in relation to specific career services at each uni but your DS needs to be aware that uni careers services, in reality, can often provide only general support. It is the self-starters who build up evidence of transferrable skills, research the opportunities and apply for multiple internships and jobs who secure the roles they want.
The 'Prospects' website provides very useful information on graduate outcomes.
https://luminate.prospects.ac.uk/what-do-graduates-do
These are obviously 'average' stats for history students and others. The more proactive your DS is, the less average his likely career outcome. So it is likely to be the case what he does with his time at either uni is likely to be the most influential factor, rather than whether there is a 'York advantage' or 'Sheffield advantage' as such.
Well done to your DS. History is an interesting and rigorous subject area and both unis have excellent reputations.