As pointed out, Aereo has not been judged legal yet, only that staying in operation until a judgement does not harm the networks. It is a good sign for Aereo but certainly not the same as done deal.
Slingbox does not just allow for recorded material, it provides live programs.
How is it different? If I am a Network I am going to say because the antenna is not at your property, and that the programming is copyrighted only to be distributed by people who pay us. Aereo in affect is distributing our material.
I'm not saying that will or will not win in Court, but there is a difference. Question is, is it enough of a difference to stop Aereo.