REST has many technical benefits, and it's not just about "style". It's an architecture, a way of thinking, that has many benefits over an rpc-style architecture. REST is also MUCH more than just a URI scheme.
REST provides 5 "constraints" that help guide toward a good API:
Self-explanatory and already the nature of web apps.
Statelessness means that state is maintained on the client. This makes every request/response transaction independent. Benefits are:
Stateless communications enable clients to recover from network errors.
Clients and servers can come and go without corrupting state.
New processing nodes can be attached without complex state management.
Cache control at multiple levels (client, server, intermediary) – because state exists in only one place. For obvious reasons caching at multiple levels decreases latency, bandwidth, and cost.
4. Layered system
Limits complexity at each layer. Also improves security because security can be implemented at multiple levels.
5. Uniform interface
Resources are identified by URIs. These URI's serve as an abstraction and should not change often. Representations are representations of a resource to the client based on a negotiation. Control Data is what negotiates the representations and actions. Hypermedia protects the server from being locked into a uri scheme.
All of these are part of REST. It's much more than a URI scheme.