Chemistry - Comparison of COSY and TOCSY for detection of small couplings between protons
The TOCSY transfer also depends on the size of the J coupling, you don't get around that.
Generally speaking it is found that cross peaks due to direct coupling build up to their maximum intensity in a time which is of the order of $1/(2J)$. Peaks which arise from transfer through two successive couplings take longer to build up, and if three successive couplings are involved, even longer mixing times are needed
Understanding NMR spectroscopy, James Keeler, page 230
The TOCSY has the advantage of creating in-phase signals instead of the anti-phase signals of the COSY, which increases sensitivity. But that doesn't mean that it is generally more sensitive.
Whether or not the overall intensity of the COSY or TOCSY cross peaks is greater depends intimately on the choice of the experimental parameters and on the molecule being studied. However, the general experience is that for small to medium-sized molecules, COSY is the preferred experiment for detecting small couplings.
Understanding NMR spectroscopy, James Keeler, page 229
I'm not sure if you can get a general answer for your case, you might have to directly compare the experiments for the kind of molecule you want to look at. You could also try longer mixing times for the TOCSY and see if they help with your small couplings (which they should, as long as relaxation doesn't eat up that advantage).