Is there an advantage to use ECO and ECO+ in respect to longevity and less stress on the battery pack since amperage is lower?
Only real use I've found is to use ECO in the rain. Compared to normal mode, the wheels are less likely to spin when I accelerate from a stop. (If I lived where there is snow/ice, I might find a similar use for ECO+.)
Aside from preventing jackrabbit starts, the biggest difference seems to be climate control. ECO reduces the effectiveness of AC/heating (still haven't figured out exactly how). ECO+ completely neuters it - the air still blows but the compressor doesn't seem to run. Just like if you run the AC/heater with the car turned on in accessory mode while charging.
In that respect, you can eek out a few more miles in ECO+ mode. But I doubt it's much different from driving gently in normal mode with the climate control turned off.
Oh. ECO+ limits the max cruise control speed to 60 mph. But if you start cruise control at a higher speed in normal or ECO, then switch to ECO+, it'll continue at the higher speed.
I suspect the presence of ECO+ is more to keep the car usable at low battery states. As the level of charge decreases, the max amperage the battery is able to output decreases. With an older worn battery which already has a lower max amperage, this decrease can cause a situation where the car is asking for more amps than the battery is able to deliver.
If you've ever had an old laptop whose battery only lasts 5-15 min, but then suddenly turns off when it hits like 60%, this is what's going on. Once the battery reaches 60%, it can no longer put out enough amps to power the laptop, so it just shuts off. Even though there's juice left in the battery, the battery is incapable of sending it out quickly enough to power the laptop.
So it goes with ECO+. By deliberately reducing the car's max power consumption when the battery charge level becomes extremely low, they stave off the car getting into this insufficient power state. And thus you're able to use more of the battery's capacity even if the pack is old and worn. And since they programmed this mode into the car anyway, they figured might as well let you enter the mode manually with a press of the button.