The general difference is that "convicted" is neutral in tone. "Condemned" includes a particular tone, and religious and moral connotations, which might be unfitting in some cases.
Edit: Take the above with some grain of salt, might be at least incomplete, maybe somewhat wrong. After consulting the internet, I've found out that there are even more meanings and nuances, which I didn't know about. Sorry for being an arrogant non-native-speaker trying to score internet points ;)
On the other hand, condemned is specifically about being sentenced to death -or sometimes life in prison or some similarly hard punishment-. Which is also why a building is said to be condemned when it is set to be demolished.
We don't ever use "sentence" in a legal context (it still exists but is old fashioned), things diverged quite a bit it seems between those languages.
Out of that context, it's usually condenado the one used.