What are different ways to determine centroids of fMRI activation, their drawbacks and perks?
This question gets close to something that might alternatively be posted to stats.stackoverflow.com. Personally, I've always felt that application of Null-Hypothesis Significance Testing (NHST) methods to neuroimaging data does a particularly good job of highlighting their scientific deficiencies. 

Personally, these days I'd use Generalized Additive Modelling (GAM) to analyze data from an individual's scan and if aggregating multiple spatially normalized scans I'd use Generalized Additive Mixed effects Modelling (GAMM). In both approaches, I'd use an AIC-adjusted likelihood ratio to evaluate the strength of evidence for differences amongst groups/conditions in the activity patterns discerned by GAM. A posteriori investigation of any evidence-supported differences can be achieved by visualization and parametric bootstrapping of confidence intervals.

If you really want to explicitly evaluate evidence for a group difference in the distance between activation areas, then one approach is to assume an a priori model for the activation, say a mixture of two trivariate gaussians with a parameter that specifies their separation, then use something like hierarchical Bayesian modelling to establish credible intervals on the difference between groups on the separation parameter.