If you are like most people, the subtle differences between these two diplomas may elude you. And naturally so, as these are defined and audited by vocational and higher education committees who have an in-depth knowledge of educational qualification frameworks. Essentially, it comes down to depth of coverage, your investment in time, degree of understanding and background qualifications and experience. 
The Advanced diploma focuses on the nitty gritty introduction to the topics. It requires you to dedicate 5 to 10 hours per week to perform at optimal level. From a qualification level perspective, the advanced diploma is pitched at the level of a bachelor’s degree in engineering in terms of understanding but with a very strong practical (or vocational) bias focussing on applying your knowledge to the job as soon as possible. You will not be covering deep theoretical concepts, but be oriented to the application of the theory. The entry level to this ranges from an engineering higher certificate or diploma to a bachelor's degree in engineering. You would benefit from the EIT advanced diploma if you are mature age (>25 years old) with good working experience. 
On the other hand, the Vocational Graduate Diploma is a relatively new but brilliantly conceptualised qualification (identical in level to that of a university graduate diploma) and is at the level of the first year of a two year Master in engineering degree.  It is oriented towards applied theory which you can apply to your job almost immediately. It requires considerably more thinking (or cognitive) ability and it is far more challenging than an Advanced Diploma. You will need at least a bachelor of engineering or equivalent or, if you are lacking this, considerable experience (typically more than 10 years working as a practising engineer or technologist) in the subject area. Full details are provided in the prerequisites section. You will need to devote at least 15 to 20 hours per week over 12 months to complete this qualification successfully. 
An example of the higher engineering level in the Vocational Graduate Diploma can be seen in the presentation of flow meters.The Advanced Diploma will cover principals of operation, installation, commissioning and maintenance, with a "touch" of some of the more advanced theory. The Vocational Graduate Diploma will cover flow calculations, standards (AGA, ISO etc) , allocation and custody transfer, meter proving, straight lengths and design along with the associated theory.