both. Some companies are building their own private blockchains while those without strong resources are building their applications on the public blockchain.
Many altcoins are utility tokens that are meant to be used on their DApps and on the public blockchains. Altcoins that are running applications on the public blockchains. Look at crypto kitties, they are running on the public blockchain.
It is resource intensive to run private blockchains and most companies are just creating DApps on the public blockchain.
In my opinion public blockchains are stronger due to their greater number of nodes or miners and running DApps on the public blockchain is much harder to hack than private blockchain.
They will still have to use Bitcoin before they can fully understand how Bitcoin works. Blockchain is only part of it.
So it will be a while till they stop using Bitcoin and begin to use their own product.