I use WolframAlpha within Mathematica; would there be any advantage to buy Wolfram|Alpha PRO?
W|A Pro over Mathematica:
- No API call limits. 3,000 for student Mathematica.
- Using Wolfram's hardward. If you run on a slow PC, tablet, or phone.
If you have access to Mathematica, W|A Pro provides little benefit. In Mathematica:
"Each Mathematica license includes a generous monthly allowance of Wolfram|Alpha function calls from within the application. Automated and non-automated usage of free-form input (= and Ctrl=), Wolfram|Alpha queries (==), the Wolfram|Alpha function, semantic functions, and entity value functions use Wolfram|Alpha API calls and are subject to the Wolfram|Alpha"
So not just WolframAlpha[] (short cut ==) uses the API calls but so does free-form input. Data manipulation is much easier in Mathematica since returns can be in Entites type.
No advantage, other than that you won't have to write the code for basic computation/visualization, which is done for you on Alpha. But you have far more control and flexibility with Mathematica.
As mentioned in the other answer, if basic analysis is all that you need, you have performance advantages with alpha, plus the hosted model, plus the app... but if you have a decent i7 laptop with enough RAM, you can do so much more with Mathematica app on your local machine.
If anything, consider a Wolfram Cloud subscription vs Alpha Pro.