Big Data, the experts say, is more about the novel way you analyze data, relative to the difficulty of the problem. A speaker at PyCon who was talking about algorithms and data structures for handling genetic data had a term that I like quite a bit better: "Data of Unusual Size" (C. Titus Brown at MSU was the speaker).
"Big Data" is a really big buzzword right now, but the term is overused and often does not convey the meaning it's supposed to. "Big" is a relative term. The novelty of how much data is being used as opposed to how much used to be used (in the sumo case, they had never handled so much data before) is what makes it big.
As for Hadoop, you'd want to use it when it's no longer feasible to keep your data stored in an RDBMS, or when speed becomes an issue, or when you want your schema to be more flexible than an RDBMS. If you are not concerned with the reliability of your data (RDBMS make the safety of the data a paramount priority--read the wikipedia page on ACID to see these guarantees), there's plenty of reasons for choosing Hadoop.
[1]: http://www.wired.com/wiredenterprise/2013/03/big-data/ [2]: http://en.wikipedia.org/wiki/ACID [3]: http://hortonworks.com/blog/4-reasons-to-use-hadoop-for-data...