Do you think the efficiency would hold using 5870's? I imagine it would be similar since the GPU's are identical.....
It likely is very similar. The 5970 likely is slightly ahead because there is some de-duplication of minor components. Also to avoid thermal overload it is my understanding that AMD takes chips from the top(most efficient) bin when building 5970s.
Still although I don't have any specific stats I would figure a rig based on 5870s should get pretty close to 2.5 MH/W.
I'd expect a 5870 may make up for the minor power difference with a higher per-core hashrate, at least at stock clocks. 5970's are clocked down a bit for the same thermal concerns.
Space being a concern for you, however, means 5970's are a better buy. They're also more widely available, 5870's are a bit hard to come by these days.