I have been working with SAP ERP solution for more than 14 years in different capacities including Developer, Functional/ Technical Consultant, Solution Architect and Project Manager. I have been involved in more than 20 different SAP ERP implementations in different industry verticals and companies of varied sizes.
There are couple of big advantages with SAP ERP. The most important one is the end-to-end functional coverage it provides. All the important business processes including Procure-to-Pay, Order-to-Cash, Plan-to-Produce, Inventory Management, Plant Maintenance, Project Management are covered quite extensively; with many possible variations in the solution and integration of all these into Financials and Management Accounting. On top of it, there are industry specific solutions for more than 25 different types of industries to address specific needs of the industry type. While most of the other comparable ERP products in market do also provide a good coverage, I think SAP edges most of them (may be only slightly on core functionalities and significantly on the industry specific solutions). Second advantage with SAP is acceptance of the solution as a global standard due to which integration with many other non-SAP solutions is much easier with SAP than other ERP solutions.
SAP also has many other complementary solutions including SAP CRM, SRM, BI, SCM which can help in achieving additional functionality. Again, integration within these solutions is much easier.
On the flipside, SAP solutions are a little rigid in their architecture and in few occasions, the desire to make the solution comprehensive has led to the solution being too cumbersome. Administering the SAP solutions, especially for large multi-country implementations is a nightmare. Another commonly heard complaint about SAP is its lack of user friendly front-end. While SAP has taken significant strides in this direction in the recent past, it still is a very complex tool and involves significant training effort (and continuous ongoing trainings) for end-users to use it effectively.
In summary, SAP is a very good ERP but needs significant ongoing effort in maintaining the solution, thus limiting its usability for small-to-medium sized organisations.