Azure SQL Database vs SQL Server on Azure VM

Compiled from numerous resources:

Topic	Azure SQL Database (PaaS)	SQL Server on Azure VM (IaaS)
Features	Less features than box, optimized to reduce costs Features that are available only in Azure SQL Database include: • Built-in backup • Auditing and threat detection • Index advisor • Query performance insight • Elastic database pools • Manage many features through Azure portal dashboard	Full box product features, optimized for the best compatibility with existing applications and for hybrid applications
Performances	Max 4000 DTUs in Premium Tier (P15)	Depends on VM SKU/Storage
DB Size	Max 4TB in Premium Tier (P11)	64TB on G-SERIES
Workload	Sizing by average usage	Sizing based on peaks
High-Availability	Built-in by platform. 99.99% high-availability SLA	Manual configuration by AlwaysOn AG. 99.95% HA SLA that covers just the Virtual Machines in an availability set
Fault-Handling	Necessary fault-handling & retry	Recommended fault-handling & retry
Locality	No co-location with application	Co-located by VMs and VNETs
Segregation	Internet exposed endpoint	Internal private endpoint
Versioning	No control on upgrades but you can change compatibility level of db.  Compatibility levels upported in Azure SQLDB V12 are: 100 (SQL Server 2008 and SQL Server 2008 R2) 110 (SQL Server 2012) 120 (SQL Server 2014) 130 (SQL Server 2016)	Full control over DB upgrade
TCO	No CapEx & reduced administrative costs (OpEx) Very low, almost self-managed. Total cost of application = Highly minimized administration costs + software development costs + SQL Database service costs	No upfront hardware costs (CapEx) Total cost of application = Highly minimized software development cost + administration costs + SQL Server and Windows Server licensing costs + Azure Storage costs
Administration	No full-time DBA required	Full staffed DBA required
Management	Easy to manage many DBs	Complex to manage many DBs/VMs
Scale-Out	Tools & Frameworks available	No easy scale-out
Configuration	No setup customization	Full access to OS and SQL Server instance level properties
Authentication	SQL standard authentication, Azure Active Directory authentication	SQL standard and integrated
Security	No Fixed IP, fixed 1433 port	Fixed IP possible, port can be changed
Backup	Backup files not accessible, 35 days Point-in-Time-Restore	Full control of backup files, unlimited PITR
Hybrid	No AlwaysOn AG support	Can join on-premises AlwaysOn AG topology
Cross-DB Access	NO: Distributed Transaction Coordinator (DTC), Linked Servers, USE statement , 4-parts names	YES: DTC, Linked Srv, USE, 4-parts names
Migrate Existing Apps	Moderate	Fast
Build New Apps	Fast	Moderate
Licensing	Not required	Regardless of VM size or SQL Server edition, pay per-minute licensing cost of SQL Server + Windows Server + Azure Storage cost for the VM disks unless Bring-Your-Own-License option is choosen
Best for	New cloud designed applications for which developer productivity and rapid time to market is important Applications using scale-out patterns Building SaaS applications Using newest cloud born SQL Database features Built-in high availability, disaster recovery and upgrade mechanisms	Running existing applications with minimal changes Disaster recovery for on-premises solutions (AlwaysOn replica) Databases larger than 4TB Features not supported in SQL Database Customized IT environment with full administrative rights Application is very chatty and requires close proximity to databases Application deeply tied to a specific SQL Server version

Also see:
Comparison of App Service, Cloud Services, Virtual Machines, and Service Fabric