For me it would be a price based issue. If I could get an Avios fare to EDI from LCY, that would decide that. If there are really good train prices in First then I’d do that. Maybe. Weekends on trains in general and Sundays in particular are often bedevilled by track work and other reasons why the thing should run at a fraction of its speed.

As the OP is going from Bethnal Green getting to LHR is much simpler with the E Line. What I would not do is go on Sleeper Trains that rock and bang all night and prevent y
ou from sleeping at all. I did it once and spent the next day exhausted.