We are using both currently.
Right now, we are just pushing shapefiles to ArcGIS Online from our Enterprise system. I am working on setting up a second server to share directly from ArcGIS Server to ArcGIS Online as you can not do this with a Federated Portal environment with IWA / PKI.
Our office is in the process of installing the ArcGIS Portal software on a development server and has been using AGOL for a little over a year. We also have the Community Analyst (CA) subscription which is now accessible from AGOL and allows sharing work from CA to AGOL and AGOL Layers are also accessible now in CA. I have many questions regarding switching to ArcGIS Portal and what would be effected if we discontinue the AGOL subscription. Any thoughts and advice would be greatly appreciated!
The agency I work for is on the cusp of using both (have been developing/testing, not in production yet), but I believe Portal will end up being the dominant platform for actually hosting and editing data given the licensing structure of AGOL. Likely we will need both for different reasons.
Thanks, everyone, for your feedback so far. I've been hearing similar remarks in ad-hoc conversations with customers and the Esri community in general: that Portal and ArcGIS both have their place, and will often be used in conjunction but for slightly different business needs.
The client which I am advising at this moment, is taking its first steps with ArcGIS Online. Due to the confidentiality and the nature of the data and the analysis they conduct they might switch to Portal for ArcGIS, next to their custom developed ArcGIS for Server applications. You're right, Portal and AGOL4O both have their place.
Kind regards, Xander