As you say IaaS gives you more control over the instance. The corollary is that you have to provide that control - and the maintenance, patching, HR, backups, DR etc... For that extra effort you get an environment exactly like the on-premise one you're familiar with, with someone else looking after the hardware.
With PaaS you lose some access (no more SYSADMIN!) but don't have to deal with many of the admin tasks either. Backups, HA & fail-over are provided to you. The experience is more like being in ops or a highly privileged developer rather than an up-to-the-elbows production DBA.
Some of the things to be aware of with PaaS are
- Restrictions on the features available.
- The SQL syntax is sometimes more limited on Azure DB.
- Costs can mount, especially at the higher tiers. If you have a terabytes of storage and heavy ingestion it can incur unexpected charges. This is easy to track through the portal, however, and you can always down-scale quickly unlike on-prem where you're stuck with the capacity you've bought.
- Things are measured in DTUs which do not correspond easily to CPU or RAM measurements. The only way to know if you have enough / too much DTU is to stress test the environment and measure performance, which of course costs money. Scaling up & down is trivially easy, however.
- There is an upper limit to the horsepower available. Looking at the pricing guide you'd have to be trying hard to stress those top-end instances, though.
- Monitoring tools you may be used to using will not play nicely with Azure DB. With an IaaS instance you can install anything you choose alongside your DBMS.
Is Azure DB mature enough? As I understand it, it is SQL Server, but tailored to a cloud environment. Rumour has it it is actually vNext and new code is first deployed on Azure, then released as on-prem CUs. So the question becomes is Microsoft's cloud ready for production, but that will be a common factor in any of the options you're considering so is moot.
Currently I work for a small start up. All our environments are on Azure and work well, though our current requirements are quite modest. Previously I've worked as DBA and developer for large multi-nationals. I would have no hesitation suggesting a heavy workload be deployed on an Azure DB.