In my experience having been both a design and an application engineer, there is no such thing as a best job for everyone, because everyone is different. A design engineer may develop a few products using a wide number of different technologies or tools. An application engineer develops a few technologies or tools used by many design engineers. As you start your career as an engineer, it is good try try a few different jobs and find out what you are the most successful at.
The perceptional problem with application engineering is that there are no direct courses at school to teach you how to be one. You learn mostly on the job, so that job seems a bigger risk. Most of your academic work has been on projects that you start and finish with a stated set of requirements, so describing what a design engineer does is easier to explain in terms of what you can see as a finished product. But the majority of products that you work on as a design engineer are going to be used by another kind of engineer to build another product. Silicon wafers are used to build generic ASIC or FPGAs that are used to build Application Specific chips, that are used to build systems that control engines, and those engines are part of autos and planes, etc. Of course those wafers are built using products designed by engineers which create endless loops of product engineering cycles.
I would define application engineering as the bridging of one product design cycle to another product design cycle. So application engineering usually involves the use of more communication skills than most engineers are usually trained to have.