Do I gain any new information by calculating both F and T statistics? In other words, if I merely want to be able to threshold voxels based on p-values, will both statistics suffice equivalently?

Basically with -fout option 3dDeconvolve spills out F for the regression coefficients, contrast tests, and full model. With -tout option 3dDeconvolve generates t for all the baseline coefficients, regression coefficients, and contrast tests.

If you are not interested in checking the full model, the F values are pretty much redundant, and in fact they provide less information than t values since F is just the square of t in these cases, plus with F you lose the information of the direction of changes. So you can just simply run 3dDeconvolve with -tout without the F values if the full model testing is not your concern and if you want to save some space both in hard drive and in AFNI drop-out menu.

Gang