Restful APIs provide some great benefits.
- Gateway's can take advantage of HTTP cache and proxy servers to handle high load.
- Complex applications can be narrowed down to simple resources
- Easy to consume no matter your scripting language.
Not all gateways offer a RESTful API. Notably Braintree and PayPal. Braintree for instance offers comprehensive libraries that make it easy to use your programming language of choice. PayPal on the other hand uses NVP (name value pairs) or a SOAP based API in lieu of rest.
The type of API offered by your payment gateway may affect your decision on whether or not you want to use their services so always check the API before you sign up.