According to the prison documentaries I've seen EU penalties in general are much lower (like half to one third) than US ones for the named crimes. And we don't have death sentences over here so that changes perception a lot.
For instance this is robbery sentence guidelines in UK [1] and CA [2]. As you can see, penalties are very comparable. Robbery in CA is 2, 3, or 5 years or 3-9 years, depending on the degree, while in UK it's 2-7 years or 7 - 12 years, also depending on the degree. The first level of robbery in UK is more attune to Petty or Grand Theft in CA. In CA there is also a GBH enhancement, that will bump you up to the 12 years, just like in the UK.
Obviously, I have not done the comparison for all the crimes, but I think if done, we would find that EU and US both have very similar penalties for all the person crimes, like theft, robbery, rape, murder, etc. Where there is a big difference is probably in the crimes that have to do with national obsessions. For US it's drugs, guns, terrorism. For EU it's WW2 and holocaust, and also terrorism nowadays. But checking drug penalties in UK I also found them to be very similar to Federal statutes in US. [3] Though, if I had to guess, I would think the UK is far less likely to apply it's possession only laws. So, that's a valid criticism.
US does have an insane incarceration rate, but it's again due to our obsession with drugs. Take that out of the equation, and we are about even. Not that that makes it all ok, but I think we are on a path to changing that.
CA is not the whole of the US. It's one relatively liberal state. What about states in the midwest? What about federal crimes? What about three strikes legislation? What about CFAA? What about death sentences? What about felony murder?
The US may be fixing some of these things but for an idea of how the US system is viewed from over here right now check out the documentaries by Louis Theroux and the one entitled "The Farm -- Life on Angola Prison".
