I didn't make the journey towards Wimbledon but did make the return.
I used 4 different apps for routing from Crook Billet to Cricklewood Broadway, starting at 20:35 and they all gave different options after the initial 200 bus, including a direct Thameslink home, SWR then Jubilee then bus, SWR then Overground then bus, District then Overground then bus.
Among the 4 apps I use Citymapper produced significant earlier arrival time than all other apps, with the fastest way home SWR then Jubilee then bus, with the District / SWR then Overground options came a close second, connecting into the same Overground train (20:52 District / 20:53 SWR).
As the Overground has a much nicer ride and connection than taking the Jubilee from Waterloo, I chose this option as well. Unfortunately I didn't make the 20:52 train after alighting the bus at 20:49 with a busy road crossing to the station, so I took the 20:57 train (I wouldn't make the 20:53 SWR too), and as I alighted at West Brompton at 21:14 I saw the Overground train just departed and had to wait for a long time for the next one, nullifying the time saving by using Citymapper compared to other apps. The District train become rammed at Southfields because of tennis .
Checking the National Rail timetable I wouldn't make that Overground train if I took the next SWR also, so I couldn't have any conclusions which line is faster.