It seems decent size capacitors can electrocute you when it's charged. Somewhere I read capacitors don't have internal resistance therefore, current is NOT limited unlike the batteries with internal resistance. But two plated of the capacitors have infinite impedance, so, is that conclusion correct? So, why are capacitors more dangerous compared to batteries
Capacitors are not necessarily more dangerous than batteries. It all depends on the specific capacitor and battery, and the voltages present on each.
Capacitors have internal resistance called ESR, equivalent series resistance. It can be in the low milliohm range, or much higher.
Batteries also have internal resistance. Not enough to save you from shock, or the battery wouldn't be very useful to provide energy to a load.
Considering that a few tens of milliamps can cause a significant shock, the voltage on the capacitor or battery and the impedance of the person and their connection to the terminals are typically much more relevant than the internal resistance of the cap or battery.
Just because a capacitor is made of 2 plates with an insulator between them does not mean that there's an infinite impedance to current flow out of a charged capacitor.
See here for more information on capacitors:
Capacitors have much higher power density than batteries, because the latter have comparatively higher internal resistance. If that wasn't so, chances are capacitors would be obsolete in many scenarios.
Batteries on the other hand have much greater energy density.
To kill a person you need quite a bit of instantaneous power but not for long, hence not so much total energy.
Therefore, given a certain size, a capacitor with suitable ratings can be more lethal than a battery of the same size.
I think that the "capacitors are dangerous" fear largely comes from vacuum tube days, where most circuits used 200 - 300 volts, and capacitors could hold that voltage for some time after the equipment was switched off.
We do still have that concern in AC power supplies, but outside the power supply, most things now operate on much lower voltages like 5 or 3.3 volts, where any voltage remaining on capacitors is not a significant concern.