Though Project online is less than a year’s old offering by Microsoft and at the time of writing this , not yet launched in Australia, it is based on a proven Microsoft Project Server technology which has come a long way over last decade and has kept pace with demands of maturing PPM practice worldwide.

Being nascent in its cloud hosted variation, Microsoft Project Online has yet to re-factor some of its features to make the product more usable and valuable for its growing customer base.

Here is a list of differentiating features which still make Project 2013 on-premise more viable solution to decision makers who are looking to gain real value out of a PPM Investment.

Business Intelligence: SSRS + direct DB access is not supported with Project online. The alternative supported tool i.e. Excel + oData has some cool uses but its quite slow and doesn’t cover many key reporting scenarios like
a.       Filtering data at query time based on user supplied parameters
b.      Very limited time phased data available and no access to OLAP cubes.
c.       Not optimized for PDF  / Print output
d.      Fetching cross project sites data is v. limited

Access to ULS Logs: The two most common error messages end users receive in Project interface are “Unknown error” and “Unexpected error”. In on-premises configuration, administrator can access ULS logs to troubleshoot the cause. In Project Online, you need to raise a support ticket to Microsoft

Controlled Patching: Project online is great because it always offers the latest software. This, however may not always be good as some times new code can change existing behaviour or worst yet, break working functionality with no advance warning. In on-premise environment, test environment can be used to control patching in planned manner.

Central Admin Access: Granular control over backing up and restoring project schedules, controlling refresh warning in excel data connections etc. are few of those settings which are essential yet being part of central admin, are available in on-premise version only.

EPMonDemand is an offering by EPM Partners (the company I work for) in Australia which offers best of both worlds by providing a cloud managed solution with flexibility & control of an on-premise solution. Having a successful track record of providing cloud hosted EPM solutions since Project server 2010, EPMOnDemand has tackled the typical challenges of multi-tenant environment by offering greater control over deployed solution based on customer needs.

Here is a full comparison list of features in Microsoft Project On-premises vs Project Online vs. EPMonDemand

Feature
Project Online
Project On premises
EPMonDemand
Administrative backup and restore for Projects (used to restore a slightly older version of a project without pulling a tape and impacting an entire organization)

X
X
Archival Environments to retain data

X
X
Multi-Dimensional Olap Cubes

X
X
Direct access to SQL Server Databases and OLAP Databases

X
X
Greater flexibility for Reporting
Direct SQL Query Access to Project Server and SharePoint Databases

X
X
Team Foundation Server Connectivity (including 2012)

X
X
Can be achieved with “YourCloud” offering.
Event Handlers can use both full trust event handlers and remote event receivers

X
X
Full access to PSI and CSOM

X
X
Access to ULS Logs

X
X
As a result of full access to the databases, PSI and CSOM there is more flexibility for Business Intelligence, Dashboards, and Reports

X
X
Recycling Bin for documents, projects, and sites
X
X
X
Project Web Applications (Add applications to PWA)
X
X
X
SharePoint Permission Mode or Project Server Permission Mode
X
X
X
SharePoint Designer for workflows
X
X
X
No database administration
X

X
Security handled by Provider
X


Latest and greatest service packs and cumulative updates
X

X
Patches tested first in internal environment
No direct access to SQL Server and OLAP Databases (Reporting is done via OData)
X
OData is not on par with direct data access


Access using CSOM (Note: PSI interfaces do not support O- Authentication)
X

 X 
CSOM & PSI, both are supported.
Event Handlers require remote event receivers
X


Extensibility is accomplished via the use of the SharePoint Extensibility Model – (as a result there is no full-trust code)
X



Reference:
Online and On-Premises Solutions for Project Server 2013 (white paper)
http://technet.microsoft.com/en-us/library/dn217893.aspx