Looking at the whole ecommerce space, 2CheckOut have always been relatively small and only ever really managed to gain a name for themselves for looking the other way when it comes to card scheme regulations. In terms of market share, they were never significant outside of a few smaller industries.
Stripe is very popular because it's easy to sign up, easy to integrate, lots of plugins available for WooCommerce and other shopping carts,and the rates are OK if you're just starting out. The same can be said about Braintree.
But for higher volumes (six figures a month), Stripe and Braintree lose their competitive edge.