@nagelc thank you for directing me to the log parser. It helped me to understand that my issue caused by lack of INCLUSION_MODE messages that is easily solved by uncommenting MY_INCLUSION_MODE_FEATURE in my gateway sketch.
The second part of the question stays valid. I realize that choosing the "right" controller is much more than choosing the controller that works good with MySensors. Anyway, I appreciate any personal experience on that.
@urbanus in your wiring, did you flip around the leds? (i.e. did you connect the longer pin to the gpio pins instead of to vcc?
With your wiring, are the leds on when there is no traffic?
My guess is that you have reversed the connections. Which is fine, but by default the leds will be on.