(이)라도 is used for more worse condition than (이)나 A(이)라도 하다 means "do A or do nothing" (이)나 하다 means "do A or do something" 빵이라도 먹을래요? => You have two options. You can eat bread or eat nothing. 빵이나 먹을래요? => You have many options. You can eat bread or something else. 영화라도 볼 거예요 => I will see movie(or don't do anything). 영화나 볼 거예요 => I will see movie( or do something else).

It is a hard question. I think there is a nuance difference though. To me, (이)라도 sounds a little heavier, meaning it sounds like the speaker has tried to think up other options but it was no use so he's now settling on this second choice. In comparison, (이)나 sounds more casual, like he/she is just trying this option on a whim without thinking much. But the difference is very subtle if any. In most cases, we can think of them as interchangeable, I think.