To me, szechuan food isn't szechuan food without the right peppers:
They have a particular type of spiciness that other peppers don't. They don't really 'burn' as much, and leave a strong minty + spicy + 'gum' aftertaste (that's a chinese word and I honestly don't know what the english equivalent would be)
Try finding an authentic place if you can, it's a totally different experience IMO. It looks like the first picture in the OP has them, but not the second.