I have Di2 on one bike, and 11 speed Athena on the other bike.

Di2
The Di2 bike is great on group rides, where I'm trying to keep up with the group's pace. I'm shifting all the time, trying to find the best cadence for the moment. I'll shift the back for just a couple of pedal strokes, since it's so simple and fast. I can even use my ring finger from the hoods. It's just like a mouse click.

I'll shift to the small chainring on even very short roller hills, instead of grinding the last dozen pedal strokes cross chained in the big ring. I can reliably shift to the 34 chainring and 3 smaller cogs in about one pedal revolution. (It shifts the front and 3 cogs in the back with one button press on each side.)

Di2 shines on faster rolling hills rides, with lots of front and rear gear shifts. It's not as big a difference on flatter roads or on very long climbs. (But even on very flat rides, I'm still shifting the rear cogs often to handle headwind changes, and small elevation changes. A mechanical shifter would do these okay.)

Mechanical
This is a triple (too bad they are almost gone now). It's my all-day ride, rough roads, or steep hills bike. On all-day solo rides, or slower pace groups, I'm not shifting quite so often. I might temporarily back off the pace and stay in the same gear longer. I like the wide range, and the 39 middle ring works great on fairly flat rides. I don't really miss the instant shifts on these rides. But if there was a Di2 triple, I'd consider getting it.

I don't shift the front as often, since it takes a long lever throw to shift to a bigger ring. Riding in the drops make it harder to do the full lever travel correctly. It's easier to shift the front rings from the hoods.