Which university is more better and famous

I got offer from Kcl and Manchester. Biochemistry in king's and biology in Manchester. I don't know how the British people think about both university and also want to know others opinions. Which one could be more better option

since you asked about British ppls opinions, I'm gonna say kcl bc tbh idt many ppl care about Manchester. I'm js giving you my opinion here, bc that's what you asked for. I'd go for kings if I were u, but you should apply wherever you feel more comfortable (eg close to family, friends, good transport links, accommodation, etc)

KCL is ranked 32nd in the world for Biology, Manchester 40th. Source: QS Rankings.
As universities overall, it's coincidentally exactly the other way around. Manchester is ranked 32nd in the world, KCL 40th.
I would say that Manchester tends to be thought of more for sciences than for arts subjects. Manchester University has had more UK Nobel Prize winners than any other university except Cambridge, Oxford, and UCL.
KCL tends to be known more for a range of different subjects but it sometimes gets overlooked in favour of Imperial, UCL and the overrated LSE. Anthropology (although Manchester's research quality is slightly higher, 85% v 86% but graduate prospects better at KCL by 18%), English (KCL 89% v Manchester 88% research quality. Graduate prospects for it are 6% higher at KCL too). Politics (although Manchester's research quality is higher - 86% v 82% but graduate prospects better at KCL by 7%), Philosophy (again, Manchester's actually higher on 84% v 82%. Graduate prospects for it are better at Manchester too, by 6%. Philosophy is actually quite a sciencey subject for an arts subject so it's not surprising that Manchester has good prospects for it), Medicine (KCL 87% v Manchester 85%. Graduate prospects slightly better at Manchester but only by 1%), Classics (tied for research on 86% but graduate prospects better at KCL by 16%), History (Manchester's actually higher 88% v 85%. Graduate prospects slightly higher at KCL but only by 1%), Mathematics (Manchester 77% v KCL 76%. Graduate prospects 14% higher at Manchester). Psychology (KCL 88% v Manchester 85%. Graduate prospects slightly better at KCL but only by 1%).
On www.thecompleteuniversityguide.co.uk, Manchester has a higher research rating (89%) than KCL (80%) for Biological Sciences, which includes Biochemistry. Graduate prospects 18% higher at KCL. Student satisfaction for this subject is near-identical. KCL is on 74%, Manchester is on 73%.
Perhaps partly reflecting that London is a popular city for international students in particular to study in, and KCL is a bit more well known internationally, entry standards for this subject are 76% at KCL, 71% at Manchester. However, entry standards for all subjects on average are closer though - 81% at KCL and 79% at Manchester. Which does suggest that KCL is regarded as more prestigious for Biological Sciences. Despite Manchester's research quality for it being higher, perhaps KCL has a larger dept? However Manchester has over 26000 undergraduate students in total, KCL fewer at over 19000. For all subjects on average, Manchester has research quality of 87%, KCL 86%.
Despite London's popularity as a place for some students (particularly international ones) to study, Manchester does have subjects that have higher entry requirements (and higher graduate prospects) than KCL. e.g. Chemistry, Physics.
It does seem that KCL is better for this course. I'd say that people from the UK probably often have a different attitude to London universities than people from abroad do. There's a general feeling that if you want a fun university experience you don't study in London. And people like to think that their university is definitely the best in their city, which is more true of Manchester.