what is better - getting an E in an a-level or withdrawing from it?

I think depends on your target university and if you meet the requirements. If you do then I doubt they’ll care as long as you provide compelling reasons for mitigation or why you performed badly. If you drop out you will just waste a year.

Why will you resit it if you didn’t even sit the exam in the first place?

Which universities/courses are you thinking of applying to?

The issue isn’t likely to be that they think you’re a “quitter” but that you didn’t study 3 A levels in 2 years. If you apply with just AA then that looks on paper like you studied 2 subjects for 2 years and then a 3rd subject for 1 year - which might be an issue for universities/courses that have heavy workloads and/or require applicants to have studied 3 subjects in 2 years.

Do you have extenuating circumstances for getting such different grades across your subjects (and that mean you’re confident that you can get an A if you study for an additional year)?

The highest courses I'd probably apply to are tech degree apprenticeships or UCL IMB (I think the contextual for that is ABC). Unfortunately I don't really have any extenuating circumstances, I was just too lazy to do my coursework and study. But I'll probably have to make up a decent reason for why I didn't complete my third A-level or got an E.

Then I would recommend that you sit the exam and see how you do. 3 full A levels with grades below what you would like doesn’t raise as many red flags as studying a partial curriculum for 2 years followed by 1 A level.