Since no-one else has replied to you I'll give you my 2 cents. I've lived in Sheffield all my life, have never been to London but am thinking of doing so for a late degree, so everything I say about Sheffield is personal experience, everything about London is research I've done in the last few months.
Sheffield is the 4th biggest UK city by population (2021 census), and it's very similar to London in that it's a diverse city with extremely rich areas close to extreme poor areas. After Bradford it's also the highest UK city above sea level, which basically translates to being one of its hilliest cities, and this is something you will notice a lot when moving between your uni buildings (both of Sheffield's two universities are city unis, meaning their buildings are dotted around the city, as opposed to campus unis where they're all in one place). The hilliness comes from its geography, but that comes with an advantage too - it shares a direct border with the Peak District, making it probably the biggest city in the UK where you have a national park at your doorstep. The comparisons pretty much end there, because London beats Sheffield in pretty much everything else - not only does it have the largest population in the UK by a mile, it's larger than the population of New York City, and according to Lonely Planet, better than it too, since it's been voted as best city in the world for the last 6 years running. It has endless jobs, opportunities for networking, sights to see, things to do, museums to visit, and so on. Pretty much the only downside of London that I can tell, as someone who hasn't yet been, is its cost.
If you only want a slightly big city, with the freedom to escape to the Peak District now and again but far less opportunities, go for Sheffield. If you want one of the biggest cities in the world and you can afford it (bearing in mind that as a student, you have the luxury of student finance taking most of the brunt), go for London.