With the ESP32’s 16-bit PWM, each step is only 0.0015%, so the LED brightness change is much smoother and almost imperceptible. This is crucial if you’re working on projects that require precise control, like mood lighting or audio signal modulation.

But keep in mind, that the lower frequency at higher resolutions might introduce visible flicker in LEDs, so you’ll need to find a balance between resolution and frequency depending on your application.

Note: UNO R3 supports 8-bit PWM resolution, not 10. 

Higher resolution means the PWM output can be more finely tuned, resulting in a smoother signal. This is particularly important in applications like motor control, LED dimming, and audio signal generation.

8-bit resolution means there are 256 possible duty cycle values (from 0 to 255). That's why the analogWrite(PWM pin, PWM value) takes values bw 0 and 255.  In this case, increasing the duty cycle step by step corresponds to a change of approximately 0.4% (1/256) of the full-scale value.

Whereas the 16-bit resolution means there are 65,536 possible duty cycle values (from 0 to 65,535).
Each step in the duty cycle corresponds to a change of approximately 0.0015% (1/65,536) of the full-scale value.

As much as the resolution is important, so does the frequency of the PWM signal. The increase in PWM resolution decreases the maximum PWM frequency possible for the same clock frequency.

if UNO and ESP32 have the same clock frequency i.e., 16 MHZ. The maximum possible PWM frequency(16-bit) for ESP32 will only be 244 Hz. Whereas for UNO(8-bit), it is 62.5 KHz. 

For example, 

16 MHz / 256 and 16 MHz / 65,536.

EDIT:

Hey everyone! Let’s clear up the confusion regarding PWM resolution and the difference between dividing by 2^n versus 2^n - 1

The Hardware Timer Perspective

In fast PWM mode, the timer counts from 0 up to a “TOP” value and then overflows back to 0.

• For 8-bit PWM, TOP = 255. This gives you a counter range of 0–255 = 256 distinct counts.
• For 2-bit PWM, TOP = 3. This gives you a counter range of 0–3 = 4 distinct counts.

Thus, in terms of raw timer ticks, there are 2^n counts per cycle.

The Duty Cycle Perspective

When calculating duty cycle, we typically use:

Duty Cycle (%)= (Compare Register Value/TOP) ×100.

• For 8-bit PWM, you divide by 255 (TOP = 255), so the highest compare value 255 yields 100 % duty cycle.
• For 2-bit PWM, you divide by 3 (TOP = 3), so a compare value of 3 yields 100 % duty cycle.

If you were to divide by 2^n directly (e.g., 256 for 8-bit), the maximum compare value (255) would give (255/256)x 100 =~ 99.6% which technically matches clock ticks but doesn’t align with the usual definition of 100 % on hardware PWM outputs.

Why It Matters

• 0 % duty cycle: Compare Register = 0.
• 100 % duty cycle: Compare Register = TOP (which is $1$).
• Users generally expect that the maximum compare setting translates to the output being fully ON (i.e., 100 %).

Summary

1. The timer truly counts 2^n steps (from 0 to 2^n−1).
2. However, to get a duty cycle percentage from 0 % to 100 %, you divide the compare value by 2^n - 1.
3. That’s why for 8-bit PWM, you’ll see many references to dividing by 255, not 256.