Idea of Sony and Microsoft with new consoles is to offer you games for rent or via subscription.

Main option will be 2 kinds of subscription.
First will be same as current one where you get few free games, but this time you will get them only for one month.
Second will provide access to pair of new top games and few hundred older ones for one month.

For all new top games primary way will be renting, price will be set per day and per week.
Most AAA games won't allow playing without constant internet connection and will keep part of resources in cloud.
Companies are expecting to increase profits 200-400% such way, similar to Adobe.

Also both companies plan to spend 80% of their marketing budgets on consoles version that is focused on cloud based streaming gaming.
It will be cheaper and much simpler. But prices will be set per hour of play, also can depend on video quality.

Considering power - both consoles will be underpowered, using 8 core Ryzen+ chip (with lowered clocks) and integrated Vega GPU (GTX 1070-1080 performance level) with GDDR6 memory of total 8-16GB. One console can use HBM, but it is low probability.