Apache Flume is well suited when the use case is log data ingestion and aggregate only, for example for compliance of configuration management. It is not well suited where you need a general-purpose real-time data ingestion pipeline that can receive log data and other forms of data streams (eg IoT, messages).
Apache Pig is best suited for ETL-based data processes. It is good in performance in handling and analyzing a large amount of data. it gives faster results than any other similar tool. It is easy to implement and any user with some initial training or some prior SQL knowledge can work on it. Apache Pig is proud to have a large community base globally.
Apache Flume is open-source so support is limited. Never the less, it has great documentation and best practices documents from their end-users so it is not hard to use, setup and configure.
Apache Flume is a very good solution when your project is not very complex at transformation and enrichment, and good if you have an external management suite like Cloudera, Hortonworks, etc. But it is not a real EAI or ETL like AB Initio or Attunity so you need to know exactly what you want. On the other hand being an opensource project give Apache a lot of room to personalize thanks to its plug-able architecture and has a very nice performance having a very low CPU and Memory footprint, a single server can do the job on many occasions, as opposed to the multi-server architecture of paid products.
Apache Pig might help to start things faster at first and it was one of the best tool years back but it lacks important features that are needed in the data engineering world right now. Pig also has a steeper learning curve since it uses a proprietary language compared to Spark which can be coded with Python, Java.
Higher learning curve than other similar technologies so on-boarding new engineers or change ownership of Apache Pig code tends to be a bit of a headache
Once the language is learned and understood it can be relatively straightforward to write simple Pig scripts so development can go relatively quickly with a skilled team
As distributed technologies grow and improve, overall Apache Pig feels left in the dust and is more legacy code to support than something to actively develop with.