I have been looking at this the last 2 days & don't think I'm any closer to a decision
the london pass with travel includes both your travel cost on buses/tube plus free admission to 35(?) different attractions
The oyster card is simply a card used for travel on the buses/tube
To figure out which one is best for us, I wrote down all the places we want to visit & if there are admission fees. Then I looked at the places to see if they are on the London pass list of 'free' admission. (The other thing I did was realistically figure we'll only get to half of those places )
Then I looked at what 4 London Pass with transportation would cost for our family versus what the admission would be to our top 5 places & I added on an extra 20 for bus/tube travel. I think for us the oyster cards at the way to go