Those has almost completely (99%) same meaning. Like you mentioned, we use them when it is not best choice. The difference in those two is,,(still I feel it's very difficult to tell even for native korean...),,
When the other just asks "주말에 뭐 할래요?", then it is more natural to say "영화나 봐요" than "영화라도 봐요"
Because we use "~라도" when it is almost final option after trying other many options,, So,, it will be like this..
주말에 뭐 할래요?
1) 영화봐요 (You say this when you really wanted to watch movie, not because any other thing pops up in your mind)
2) 영화나봐요 (It's like.. I don't have any special plan either, so why don't we just watch a movie?)
3) 영화라도 봐요
You can of course use this one for situation 2), but,,, you can also say this in below situation
A: What are we gonna do in weekend?
B: How about driving out to XXX?
A: Sound nice, but the traffic will be crazy..
B: Hm,,, how about XXX?
A: I don't think that is good idea either because bla bla..
A: Let's go to see a movie then. (영화라도 봐요)
B: Yeah,, that will be nice.
(죄송합니다. Base 언어도 한국말인걸 지금봤네요... but I think you can understand above explanation)