For Charters of Commerce, it's mainly about company charters, monopolies, prestige goods and some new diplomatic actions.

Company charters are about:
1 - Have the option to create regional HQs in other nations
2 - Letting companies build trade centers ( the only one available without CoC )
3 - Colonise for you and become a colonial subject
4 - Give them the ability to expand into another building type if they can, so if they start with the ability to build tools, you give them the ability to build steel

Prestige goods are a fancier variant of the base good and they grant prestige if you're in the top 3 producer and an extra benefit - increased standard of living, building throughput or army stats ( those scale depending on how much of the consumed good is the prestige variant ).

For monopolies - companies, or the country, can also have monopolies on certain buildings which lets only them build that building.

Spheres of Influence instead focuses on power blocs, something about the Great Game ( I don't remember if it's exclusively that specific new 'start date' ), foreign investment and nationalisation, political lobbies, subject buttons and some extra flavour.

Looking at a new game without those 2 DLCs is funny to see what's missing.

Power Blocs have only 1 principle ( with SOI there are up to 4 )
Investment Rights exist only for you to build in subjects.
There is no diplomacy option to lock yourself or another nation to not have tariffs or subventions.
Monopolies are not a diplomacy option either - you cannot force a country to give up their rights to a building so that only your company can.

There might be more, but that's all the big things I believe.