Great question.
Which tool you need, or both, depends on what your final product to end users is, and how you built it up.
In this case, if there is a multi-tier application that includes a Web client and mobile clients, and also uses your own APIs, then yes my best recommendation would be to get both tools.
Load testing APIs make sense when they play a core role in the system, and you have established that it is a key factor in the overall system performance.
Note that as you record scenarios for tests with loaduiweb, all HTTP traffic will be recorded, including requests/responses to the API end points. So, when you simulate your Web client scenario in the context of load testing, your APIs will be effectively simulated as well, certainly. However, you won't be able to determine specifically the load capacity of the APIs directly, only inasmuch as they are involved in the Web load test you are performing.
There are options for directly load testing certain types of APIs (e.g. SOAP over HTTP web services) with loaduiweb, please refer to the tool's documentation. They are a bit more restricted than what you could do with loadui.
Hope this helps.
