I have an older Gigabyte with a 1070 MaxQ. Runs well. Thats all I can say regarding the GPU as I never used a 1060 model.
Hoewever I noticed the 2060 model is the stealth version by MSI. My older laptop (GS43 or 44), now owned by a friend, was from that line. I liked the understated look of it more then the full blown “RGB rainbow gamerfied” version. Mt colleagues still amde fun of me though for the red keyboard :D. Additional the upgrades were easy to do myself, like popping in another ssd/nvme. It ssems the GS still has the same feature, couldn’t find anything on the GE (not mentioned on the website or in any review).
The 2070 model has another advantage though, 30% more ram over the 2060 (8GB instead of 6GB), it seems to have more ports and is stlightly thicker. The GS cooling structure seems to have been upgraded over the GEs, as the GS is thinner so it would need better cooling. However it seems to me that they mostly just increased the airflow (3rd fan, thinner blades) and pressure. For me that would indicate potentially higher noise,potentially higher pitched fan nise too (higher rpms and fin density).
The GE has FAR better port (placing), power and the RJ45 are on the back side, as well as mini dp. In general more ports thanks to the larger size. The GS66 has its rj45 on the right side, were the mouse is if you are right handed; WHY? The power is on the left side though, thank god for that.
I think it comes down to usage, the GS66 were always slightly smaller, a tad lighter (200g) and understated, wheras the GE series sort of a middle of the road model with a more gamer look to it.