The best system varies based on the kinds of questions you want to answer. You will need to be a bit more specific about your project. Are you interested in quantifying biomass in residue? Interested in types of tillage practices? What types of crops are you examining? I suggest reading some of the literature.

Daughtery has done a lot of research into estimating crop residues.

http://www.sciencedirect.com/science/article/pii/S0167198705002849

https://dl.sciencesocieties.org/publications/aj/abstracts/97/3/0864

There was some recent research by some of my colleagues at Virgina Tech and the University of Oklahoma.

http://scholar.google.com/scholar_url?hl=en&q=http://www.researchgate.net/publication/232709561_Remote_sensing_of_crop_residue_cover_using_multi-temporal_Landsat_imagery/file/9fcfd50cb8af51ce73.pdf&sa=X&scisig=AAGBfm26IY_RLLA-Vf4Hk3EJKghmiLeXlQ&oi=scholarr

Article Remote sensing of crop residue cover using multi-temporal La...

Good question! I would suggest using hyperspectral data between 2000-2500nm to detect lignocellulose absorption. That would unambigously enable you to map crop residues.

The good satellite data for crop residue mapping is that which have the ability to discriminate between crop residue and the surrounding environment such as soil type and characteristics. It is also important to look closely at the crop type. I agree with the above answer, you need hyperspectral data.

Hyperspectral data is good but not feasible for many projects because of high data costs associated with acquisition, data storage, and processing. It is better to determine which bands are optimal for a variety of uses and then use those bands in future satellite systems. Since the original post asked for which satellite system was ideal. I am assuming we are talking about current satellite sensors, which is quite limited. Hyperion has a very limited data set and requires requests that are prioritized meaning that your particular research may not be conducted.

I agree with the above answers, hyperspectral data is the best option, but not feasible in many circumstances because of high cost and small footprint. It is worth to trying Landsat data , since a few researches on crop residue using them have demonstrated success at a certain degree (e.g., McNairn and Protz, 1993; Van Deventer et al., 1997; Biard et al., 1995; Bannari et al., 2000).