As a designer I may be a bit biased but I do appreciate the value each provides. Landscape architects are left-brainers with strong math and science skills. Where some may lack in plant knowledge and artistic sense they excel in long range planning. If you are starting with a new home they will know how to grade the yard to avoid drainage issues and make sure you have room to get the car out of the garage. A large pool project with a multi-level hardscape might be an appropriate time to use their services.
Designers on the other hand come from a variety of backgrounds and typically aim for a more artistic result. Usually they will be more aware of new plant varieties with improved characteristics or bloom sequencing to make a garden perform well through the season.
There is quite a bit of overlap and either will help you avoid novice mistakes. Aesthetics are a matter of personal taste so always look at some examples of past work to find the best for you.