My 2 cents. Others may disagree, given their particular orientation. Given a choice, we are in Decision Science domain; Given a firehose we are in Data Science domain. I would suggest that Decision Sciences ends where Data Science begins. Decision Scientists don't necessarily work with Big Data. Data Scientists are specialized to work with Big Data (or recognize when something isn't truly Big Data) and all the problems associated with that domain.
Decision Scientists build decision support tools to enable decision makers to make decisions, or take action, under uncertainty with a data-centric bias. Traditional analytics falls under this domain. Often decision makers like linear solutions that provide simple, explainable, socializable decision making frameworks. That is, they are looking for a rationale. Data Scientists build machines to make decisions about large-scale complex dynamical processes that are typically too fast (velocity, veracity, volume, etc.) for a human operator/manager. They typically don't concern themselves with whether the algorithm is explainable or socializable, but are more concerned with whether it is functional, reliable, accurate, and robust.
When the decision making has to be done at scale, iteratively, repetitively, in a non convex domain, in real-time, you need a Data Scientist and lots of compute power, bandwidth, storage capacity, scalability, etc. The dynamic nature of the generating process which leads to high volume, high velocity data, in my mind, is the differentiating factor between the two domains.
The transition from manually input data sources to sensor-driven real time data sources is the underlying theme of the "Internet of Things" and this is especially true with the "Industrial Internet of Things" with complex machines interconnected with hundreds of sensors relaying data continually. The underlying math may be somewhat sharable, but doing it at scale, at velocity, etc. requires an end-to-end approach, and a greater emphasis on high speed algorithms. This is particularly true when you are talking about IoT, and especially IIoT, where you do not want humans to be making decisions "on the fly".
A Decision Science problem might be something like a marketing analytics problem where you are segmenting a customer base, identifying a high margin target market, qualifying leads, etc. Here the cost of a bad 'decision' is relatively low. I view Decision Science from the perspective of "decision making under uncertainty" (see Decision theory) which suggests a statistical perspective to begin with. A Data Science problem might be more like "How do I dynamically tweak a Jet engine's performance in flight to ensure efficiency/uptime during flight, to achieve stable and reliable output, to optimize fuel consumption, to reduce maintenance costs, and to extend the useful service life of the engine?" The cost of a failure in flight can be pretty high. Here, you would want to have a reliable machine making those computations and decisions in real time, relying on both ground and in-flight streaming data for real time condition monitoring.
In reality, practitioners tend to be "Agnostic" Scientists that are transferring skills from one domain to another, with varying degrees of comfort with the different tools out there. However, a Data Scientist is more likely to have a diverse background that spans multiple disciplines including statistics, computing, engineering, etc. In these examples, the decision maker is a key differentiating factor in my view. A Decision Scientist typically provides a framework for decision making to a human being; a Data Scientist provides a framework for decision making to a machine.
When machines become more human, this distinction may be called into question, but for now, I think it works.
What do you think? Did I just give you a choice? Or, did I just deluge you with data? Your call.
Note: In the above marketing analytics example, I am not referring to clickstream data; rather, I refer to historical records stored on an RDBMS somewhere.