3 August is coming towards the end of the Summer School Holidays, so people are away in any event. Domestically within Scotland the Monday may be busier for travel, but not really on Anglo- Scottish routes.
If folk were going away specially it would have been after work on Friday or on Saturday morning- which is the traditional vacation weekly switch over day. There are heavy cross border flows on a Saturday to the seaside resorts in Lancashire and Yorkshire.
If there is heavier traffic on the Monday cross border it will be north from those English resorts late morning to afternoon.
The other flow to think about on the Sunday is the substantial flow of Scottish workers to London- it really is a significant thing- pm Sunday to London, pm Friday to Scotland. A flow I used to be part of, and when I traditionally used to upgrade to 1st class on Sunday due to how busy the trains were by Carlisle heading southbound.
We don't know this far out how whether there will be rail engineering work on the Sunday- but either the east coast route to Kings Cross or the almost equally fast west coast route to Euston will be open, both can't be closed at the same time due to cross industry agreements.
Also now that the LNER trains from Edinburgh are fast Newcastle-York-London in the main, traffic to intermediate destinations (other than London) is likely to be more on the Cross Country and Trans Pennine Express stopping trains.
LNER services to other English destinations, like Durham, is now generally served by a Newcastle to London 5 car hourly train
So on balance I think Monday 3 August is preferable to Sunday 2 August.
