I'll answer your question, but go do your own work and research it yourself ffs. They're very different degrees, and if you dont know the difference you haven't looked into it enough yet to be considering places to go study it. With that attitude, you won't hack any biochemistry / biomedical course, you aren't spoon fed. Its damn hard.
Anyway, to save the multiple down votes i'll shove you in the right direction atleast.
Biomed / biochem and neuroscience are all very respected courses. People will ask you what you study, you'll tell them biomed, and they'll go, oh jheeze that must be well tough. So you get the point.
Biomed = the research behind medicine. The people who conduct the cures for HIV and cancer and pretty much every other drug you can think of. Microbiologists, immunologists, haematologists, toxicologists, virologists, clinical biochemists are all potential careers directly relating to biomed. Aside from this its a well respected degree, and you learn many different transferable skills, maths, essay writing, statistical analysis. Significantly more biology than chemistry.
Biochem = similar to biomed, but with a more chemical basis. Less based on medical microbiology and immunology, more based on enzymes and how structure and function of proteins and the properties of amino acids give rise to how enzymes within the body actually perform their functions. Heavily based around clinical biochemistry, glycolysis, enzyme interactions, amino acids, lipids, also can encompass developmental biology in some unis too.
Neuroscience = study of the brain. Cross between psychology, developmental biology, and neurology. Can't say much more as I don't study it, and only know a few people who do. Less based on chemistry, more based on the psychology aspect of biology. Cognitive psychology, biological psychology etcetcetcetc. If you like psychology, but want to do a more well respected course with a more clinical scientific aspect, do neuroscience.
Other options include genetics, which is pretty self explanatory, straight biology, (if you get off on bugs / plants/ trees / photosynthesis / evolution its for you), and straight chemistry, which in my opinion would be suicide inducing, but hey ho if you love atomic chemistry, and chemistry A level and want more of that, bonding etc go for that. Both biology and chemistry are significantly less clinical. So if you want to do med, do biochem / biomed.
If you want a **** tonne of money though, dont go into science. Go into corporate banking / accountancy. Its less job satisfaction but you'll be paid more, work in a fancy office probably doing the same thing every day. But everyones outlook on what they want is different.
I go Sussex and love it. Don't go on league tables alone, i know people who did and then lived to strongly regret it. You probably won't take this advice, no one on TSR ever does. All people on here care about is oxbridge and russell group. But hey, go look at unis you like, then make your own decision.