The goal of rivens was to make older, less powerful weapons, useful again.
Rivens CAN work, but usually don't. There are just some weapons that no amount of crit, damage, multishot, etc. that would help. Like the Acrid for example... I've tried...
It DOES work for some weapons though, that just aren't part of the meta (i.e. Slash procs and explosions), so they get stronger, but not enough to bring them up to the power levels we have nowadays.
Incarnon adapters change the base stats of a weapon and add an alternative firing mode, making the weapon stronger in general.
As an example, my bo riven has damage, attack speed and crit damage with negative finisher damage. It made the bo strong, and I used it allot. It never really impressed me until I added the adapter.
Overall, adapters are more useful than rivens if the goal is to make underpowered weapons useful again. I have a ton of rivens, but the adapters add more value to a weapon, so I guess I prefer the adapters.