With the announcement of Power BI at the WPC last week, Microsoft now has *two* ways it can host your BI application in a public-cloud setting.
We're still very early in the game, of course. Azure IaaS is still pretty new, and Power BI has a few months and some rigorous testing before it's released. So my guidance here is far from complete.
However, it does make sense to think of the scenarios where one approach may be better than another. At present, I find it may be a stretch to see many "better-together" stories (i.e. where BI is provisioned through both Azure VMs and Office 365) - but I'm sure an exception or two will pop up.
Here's my first stab at rationalizing the choice - I'm sure the thinking will need to evolve over the coming months.
Supported by Azure Virtual Networks; no specific list of data sources permitted/restricted; does require on-premise firewall configuration
No built-in "app" at present; can always provide browser-based access to SharePoint BI capabilities
2GB (as dictated by SharePoint)
No Integration Services, Analysis Services (OLAP or BISM), Master Data Services, Data Quality Services, Reporting Services (aside from Power View),
PerformancePoint Services, Visio Services
All SQL Services (SSIS, SSMDS, SSDQS, SSRS, SSAS) can run in an Azure VM, as can PerformancePoint and Visio Services
Available at GA
Not immediately available
Very quick setup; little involved with creating a Power BI site in Office 365
Pre-built Azure VMs for BI workload not currently available. Similar architecture/configuration considerations vs. private cloud deployment
New Power BI SKU (requiring E3 and Office Pro Plus coverage for audience) - no explicit license for SharePoint servers or SQL Server capacity
Requires Office Pro Plus, SQL Server (Enterprise), SharePoint (servers and eCAL) - no Power BI SKU considerations.