STAAD Pro is a general purpose software that can be used for any type of structures like Bridge, but ETABS is customized to analysis and design buildings. In that purpose Staad Pro can be compared to SAP2000 as it can be used for all types of structures.
If we want to compare Staad Pro & Etabs for building design purpose then we can compare like below:
1. Etabs is very easy to model a building as a remarkable time saver. STAAD Pro uses the same user interface which was implemented for DOS to retain the large existing user base. It does not use windows OS user interface advantages. Because of it, the user interface is not consistent, not object based which makes it to difficult for new users to learn. One example, you cannot select physically one support and change its boundary conditions.
2. We are in the era of structural information modelling, Building information modelling etc. some people are still appreciating STAAD editor which is ancient method of input ( Even SAP90, predecessor of ETABS was using this input method), as upgraded era of structural design Etabs is better to use with API for complex structural building modeling.
3. ETABS offers structural information modelling where you will only model structural data and Finite element data are generated internally. For example if you introduce a hole after meshing a slab in STAAD, you need to delete and re-mesh, but no need to do that in Etabs as it does automatically.
4. You can do object based editing in ETABS and not easily with STAAD Pro. Using assign command after modeling elements without any property is a time consuming way. We can use the property editor widely used in windows, but no comfortability for property editor dialog.
5. Presentation of results in ETABS is much better than STAAD Pro. Auto-meshing is way more accurate, plotting stress contours and checking the result is way more easier.
These are the major differences collected from the Expert opinions on Quora Answers to the Similar question.
You may check following video regarding differences between Etabs & Staad Pro.