Is there any difference between "beat up" and "rough up"?
As far as I understand, the two expressions are synonims. But is there any difference between them? I don't know why, but to me 'beat up' sounds like someone has been beaten up by a bunch of people really badly and for a long time. And 'rough up' sounds like someone just got a few punches. But this is just a guess!

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Answer

Yes, you're right. They are basically synonyms, but "beat up" sounds more severe. "Rough up" might be the same but could also just mean they were pushed around aggressively, for example. However, "beat up" doesn't mean there was a large group necessarily. Either one can be done by one person or a group.

Hope this helps!

Answer

I think, in American English Slang,  ‘ROUGH UP’ is often used with:

a  sense of Premeditated Implied threat
a  sense of Premeditated Punishment
or the implication of teaching a violent lesson ..

"The Mafia Don sent his guys to rough him up a bit.” 
"The prisoner claimed that he was roughed up by the guards."

Whereas "BEAT UP" is a more generic term. 
BEAT UP :  If someone "Strikes ( a person or an animal ) repeatedly and violently so as to hurt or injure them".. 
I think there's Less Implied Nuance than 'ROUGHED UP'..

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