Is the EC50 of an activating protein for an enzyme a good indicator for the binding affinity Kd?
You can certainly get massive differences between EC50 and affinity. This is especially true for cell-based assays and membrane protein systems. 

The reason why is because the appropriate time scales to achieve binding equilibrium (hrs for nM affinity, days for picomolar, feptomolar affinity according to back of the envelope calculations) may be and likely will be different from the appropriate time scales of activation, endocytosis, degradation, etc. Furthermore, you can have avidity effects that would not be apparent in a dilute membrane assay compared to a cell's surface. It could very much be that the dominant terms in mass transport change depending on the geometry and antigen density and while I'm not entirely sure bout vesicles vs. emulsions it is true for cancer models. Theoretical analysis of antibody targeting of tumor spheroids: importance of dosage for penetration, and affinity for retention.


Case study number I: hGH:hGHR interactions have been extensively studied and high affinity hGH have been produced. However, none of the variants showed improved EC50. It turns out that the binding was primarily influenced by the off-rates which were so slow, that affecting those values did little to the kinetics of the system. Growth Hormone Binding Affinity for Its Receptor Surpasses the Requirements for Cellular Activity

Case study number II: CEA-antibodies have been affinity matured to have pM activity compared to the wild-type nM affinity. However, the antibody had minimal effect on tumor uptake. As CEA gets endocytosed on the order of 30 minutes, all of the antibody was simply getting endocytosed rather than acting as an inhibitor. Directed evolution of an anti-carcinoembryonic antigen scFv with a 4-day monovalent dissociation half-time at 37°C.

(edit)
I realized that this answer is more applicable to IC50s vs. the EC50 experiments described above. However, many of the points remains. The Km between a substrate and its enzyme is a thermodynamic property where as the EC50 also has dynamic factors that may influence its measurement.

I would also add that simply adjusting the pH 2 units may result in a 2 orders of magnitude change in activity.

(edit2)
A further point to make about enzymatic assays is that from an observation of Michaelis-Menten kinetics, the KM of the reaction isn't the KD of the enzyme but alternatively the effective binding constant.

Recall that:



If there is a non-trivial kcat comparable to the dissociation rate kr, the enzyme will have an effective half maximal concentration that is significantly higher than the Kd. There are multiple ways how your assay can result in the discrepancies that you're seeing. The first would your strategy in measuring your EC50. If one is an enzymatic readout and the other is a binding readout, you would naturally have very different results.  Alternatively, the enzyme in the detergent system may be catalytically more active than the vesicle system resulting in a higher effective KM. Again, the pH thing.

Finally, there is always that awkward moment when you realized that you might accidentally have measured a titration curve rather than a binding curve.