HS1 does nothing for London Metro routes really and crossrail helps 1 out of 6 Metro lines.
Crossrail isn't just about commuting, something we all seem to forget.
Crossrail is going to provide a lot of choice and opportunity for that part of Kent and indeed South East London. Destination is very important. The close and very direct impact will absolutely be anything going through Abbey Wood. That is services via the North Kent, via Greenwich, and the DLR out of Woolwich. What is also impacted is Dartford and stations beyond. People travel from Dartford and into Lewisham/Charing Cross/London Bridge to interchange to the Tube. Everyone making some kind of cross London connection can now make a decision on what line to take. That will impact all 3 lines out of Dartford. It also reduces the crowding and congestion at Lewisham, which impacts all lines.
What will also happen is that local traffic will alter significantly. Not just the local bus network but cars. Station car parks are full and many people will travel by car and then travel into London. I suspect that many people will adjust their starting point when Crossrail kicks off. Abbey Wood and Woolwich pull in traffic from a large area of South East London.
For me, I'm looking at journey times. I am a mostly a leisure traveler when I use the train and a service that takes me right into Tottenham Court road is very very tempting. I'm sure others looking at the map see other opportunities too. What is also important to note is that big giant link to Heathrow. That will influence travel too.
I think what we also have to consider it not so much about how much it will ease each line but how much it will generate travel into Abbey Wood/Woolwich.