You're blurring a few topics here
1) cloud vs premise
Makes no difference to your skillset. Whether your Oracle database is in the server room next to your office, or in a server room 2000 miles away, its still an Oracle database.
Check out
https://cloud.oracle.com/home We've got products left, right and centre to cover all sorts of levels and need.
2) relational vs nosql
You'll hear a term "polyglot persistence", which is hip and trendy way of saying "right tool for the right job". A relational database gives you ACID, read consistency and many other cool things. For my financial transactions - man do I want that. But for (say) my application logs...I can probably live without ACID - I dont care if I drop 1 out of every 100,000 logs. So perhaps I'll use a NoSQL solution for that (and yes...we've got one).
3) data vs bigdata
I hear this all the time: "Facebook uses X, so we should use X", "Google uses Y, so we should use Y".
That is totally fine ... if you *are* Facebook or Google, or are going to be be the *next* Faceook or Google. If you need to store petabytes of video and photos, and your company is 50% software engineers, then by all means.... Cassandra is quite possibly your best bet.
But if you are like 99.99999% of customers who have data requirements not at that scale, then a relational database, and perhaps some NoSQL technology will be absolutely fine for you.
And whether that technology is on site, or in the cloud, or anywhere else for that matter...makes no difference to the need for expertise to utilise it intelligently.