We can only hope that TfL improve their finances, and their begging bowl is looked upon more favorably. Byford will help this along, I'm sure - I hope he gets on better with Khan than with Cuomo, but the sad fact is that the current Tories will be obstructionist to a Labour Mayor.
In reality, both play a big role.
A combined NLL/WLO station, ideally four tracks/platforms - which covers the full NLL, routes down to Richmond, Kew Bridge (!) and Hounslow and across the North Circular arc. Much more about local connectivity, employment and so forth. But also bringing a lot of SW/W/NW London to HS2 and Heathrow access.
A WLL station (ideally with Southern, but viable without, ie. Hythe) - which is more about regional connectivity and accessible to inner West London (inc Shepherds Bush) and useful as a spread of traffic originating from the NLL. Now to stitch it up with GOBLIN
