Is there a difference in meaning between 应变能力 and 适应能力 in this sentence？ If so, can you please try to explain it?
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應變 is a response to an emergency, or something unexpected, as in 中央災害應變中心 National Disaster Response Center. 變 here is not 變化， but 事變. 應變能力 is emergency or incident response capability. One sees this in cyber security a lot, also in the American FEMA agency. It has nothing to do with "adaptation".
I think the catch here is the 'time frame' of the changes:
Take your sentence, 在未来十年的商战中，最重要的武器是应变能力、适应能力, and some examples:
Assume the company never used the new cloud service - everyone's saving stuff on their local computer. The new cloud service will be introduced to the company, where everyone has a chance to start learning about it. In this case, your capability to adapt the changes - 适应能力 - is required. You are not required to act immediately, but to slowly adjust to the new system.
Assume the company is a logistic company, where a huge shipment being delivered is lost due to an accident happened last night. You, as the manager, has to prepare the shipment from another office, thus fulfilling the delivery. In this case, your 应变能力 is required. You have to act/ react immediately.
Both cases describe a changes where one happens over the years and the other one happens all of a sudden.
应变能力 and 适应能力 look similar, but they do not have the same meaning. 适应 has to do with adapting to a more or less static environment, for example, if you move from one part of the world to another, you need to adapt to the climate of your new home and you need 适应能力. 应变, on the other hand, introduces an element of unexpectedness. 应变能力 is your ability to react/ respond to (usually unexpected) change in the environment. In your example sentence, the company needs both 应变能力 and 适应能力.