How do you plan to access your database engine in the cloud?

If you go down the IaaS route then you install SQL on a VM and everything is just the same as running in your own data centre. This applies to just about any IaaS vendor. However, each vendor has its own set of pre-defined server configurations so the main thing you need to review is how your workload fits in to their offering.

If you use the PaaS route then there may be some limitations on the features you can use. For example Replication and AlwaysOn are not often supported. Different PaaS vendors offer different capabilities, so your first step should be to match your organisation's needs against the various PaaS offerings.

Both IaaS and PaaS are mature offerings. You should have no more concerns about using these than you would have about any move to a new data centre. If your organisation is seriously considering going to the cloud then talk to the potential vendors as there is often pre-sales support (just as there would be if you were thinking about a different data centre).

My employer moved all their production systems to AWS IaaS in 2012, and currently serve over 4m page impressions per day out of AWS. The greatest business gain for us is flexibility - no matter what we want to do we only have to consider the marginal costs which means we can get new stuff to the market faster. We also saved about 25% of our hosting costs and have a more stable service but for us the flexibility is what we mostly talk about.