The worst so-called 'automatic' cars are the budget hatchback ones - mostly sourced from India - that have an 'Automated Manual Transmission' (AMT) fitted - which in essence simply removes the clutch pedal from a normal manual 5-speed gearbox & replaces it with an electronic control unit (ECU), usually supplied by Magnetti Marelli, that takes over the engaging / disengaging of the clutch mechanism and the gear selection via either an electronic or hydraulic (pneumatic) servo system.
Some cars, like the various Suzuki models fitted with an AMT, still have a manual gear change 'over-ride' feature that allows you to down-shift / up-shift the gears manually if so desired, according to driving conditions, like going up or down a steep mountain pass like Kloofnek.
Others however, most notably the Renault Kwid 'Easy-R' AMT models (both pre- & post-facelift versions), only have a rotary 3-position gear selector dial for 'Drive - Neutral - Reverse' and NO manual gear selection over-ride capability.
Kwid AMT Pre-face-lift - centre upper dash console mounted gear selector:
Kwid AMT Post-face-lift - centre lower centre console (between front seats) mounted gear selector:
All of the reviews of these AMT cars make mention of the hesitation & sluggish up- & down-shifts, and the 'head-nodding' that results when the AMT finally does change gears.
These are all just a cost-cutting compromise rather than spending extra on actually fitting a 'proper' automatic, whether that be a CVT, a DSG or a conventional torque-converter unit.
So it all boils down to the individual driver preference:
Do you want to 'row your own gears' ALL the time? - get a manual (as long as the brand you are wishing to purchase still gives you that option)
Do you want the convenience of the car changing gears for you, with the option of still doing it yourself if needed (Kwid excepted), but still want a budget economy car? - get an AMT
Do you want the car to change gears for you, without noticing the changes at all and eliminating the 'head-nodding' effect? -get a CVT
Do you want a choice of a multi-gear automatic (usually 7-speed to 10-speed) that still lets you change gears manually if needed, especially when towing trailers? - get a Torque-Converter automatic
Do you want instantaneous performance-orientated gearshifts for those inevitable robot-to-robot 'boy-racer' VRRRRR-PHAAAA drag races, or for sporty track-focused enthusiast driving? - get a DSG
You get what you pay for - the more you are willing to spend - the more choices are available to you.