How do bargain basement modern digital meters perform compared to
the old analogue meters from 30 years ago like the AVOmeter?

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Thirty-odd years ago my friends had AVOmeters. I would look on
with some envy. Remember AVOs? I think they were mainly a UK
thing. 10 by 8 inches and about 4 inches thick. See this:-
http://www.richardsradios.co.uk/Images/AVO.jpg

Today I can buy a regularly stocked item like the super-cheapo
single-chip digital multimeter from a UK shop like Maplins for £8
($8) and that includes the battery. Although Maplins call it a
"domestic tester" it is more than just that:

600V-200V-20V-2000mV-200mV plus 600VAC-200VAC
10A-200mA-20mA-2000uA-200uA
2000kO-200kO-20kO-2000O-200O
transistor and functions
overall accuracy approx +/-0.5% to +/-1.0%

http://www.maplin.co.uk/module.aspx?ModuleNo=37279&doy=26m6

How does something as ridiculously cheap as this meter compare, in
terms of measurement accuracy, to an old stye AVOmeter?