Key differences between Azure DocumentDB and Azure Table Storage

I consider Azure Search an alternative to Lucene. I used Lucene.net in a worker role and simply the idea of not having to deal with the infrastructure, ingestion, etc.. issues make the Azure Search service very appealing to me.

There is a scenario I approached with Azure storage in which I see DocumentDB as a perferct fit, and it might explain my point of view.
I used Azure storage to prepare and keep daily summaries of the user activities in my solution outside of Azure SQL Database, as the summaries are requested frequently by a large number of clients with good chances to experience spikes on certain times of the day. A simple write once read many scenario usage pattern (my schema) Azure SQL db found it difficult to cope with while it perfectly fit the capacity of storage (btw daily summaries were not in cache because of size) .
This scenario evolved over time and now I happen to keep more aggregated and ready to use data in those summaries, and updates became more complex.

Keeping these daily summaries in DocumentDB would make the write once part of the scenario more granular, updating only the relevant data in the complex summary, and ease the read part, as the capability of getting parts of more summaries becomes a trivial quest, for example.

I would consider DocumentDB in scenarios in which data is unstructured and rather complex and I need rich query capability (Table storage is lagging on this part).
I would consider Azure Search in scenarios in which a high throughput full-text search is required.

I did not find the quotas/expected perf to precisely compare DocumentDB to Search but I highly suspect Search is the best fit to replace Lucene.

HTH, Davide