For a static subject in steady light they genuinely produce the same picture, which is why your test showed nothing. The differences appear in specific conditions.
Electronic shutter advantages:
- Silent. No moving parts, no sound at all. This is transformative for theatre, ceremonies, wildlife and anywhere a click is intrusive.
- No vibration. Nothing moves, so there is no shutter shock softening long-lens or macro shots.
- Very fast top speeds and high burst rates.
- No mechanical wear. Mechanical shutters have a rated life measured in actuations.
Electronic shutter problems, and these are the ones that catch people:
- Rolling shutter distortion. The sensor is read out line by line rather than all at once, so anything moving fast across the frame is skewed. Propellers bend, golf clubs curve, a panned car leans.
- Banding under artificial light. Many light sources flicker, and reading the sensor progressively records different brightness on different lines. You get horizontal stripes.
- Flash is usually unavailable or severely limited.