SQL Azure is a great choice for hosting Sitecore’s databases. Out of the box it provides many features like high uptime SLA, performance you can adjust easily based on demand and geo-replication. Since Sitecore 8 you can publish your databases to SQL Azure without any schema changes.
If you are using SQL Azure for a while you might notice that your Sitecore’s performance might go down over time especially at times when the database gets hit hard for example right after an application pool recycle. I initially had many incorrect assumptions regarding the source of these issues, I looked into prefetch cache, additional content, site traffic etc. Eventually i figured out that i had to update statistics and query plans which immediately resolved this issue.
This issue is not specifically related to Sitecore only but can be experienced with other technologies as well. However be sure to update statistics regularly to avoid any unnecessary performance issues in your site.