It seems easy to jump to the conclusion that people who have dom/aux Fi would be more driven to do something because it makes them happy while those who have dom/aux Te would be more driven to doing something because it fulfills reasonable goals. However, this seems like a weak interpretation of how the functions play a role in what motivates us, since "reasonable goals" can include wanting to attain happiness and life satisfaction, so even dom/aux Te-users might be equally driven or more driven than dom/aux Fi-users to do something if it makes them happy. So in that case, BOTH Te-users and Fi-users are going to be equally driven to do something for the sake of personal happiness, more so than if it would fulfill reasonable goals.
Instead, I believe the main difference between Te-users' and Fi-users' motivating factors are HOW they want to achieve personal happiness. Te-users are more likely to achieve personal happiness more methodically and often logically, usually with a reasonable basis for their methods and strategies to pursue what makes them happy; they are often focused on their methods to achieve what they want. Fi-users, on the other hand, seem more likely to achieve personal happiness by taking a more open approach to their methods to achieve it, less focused on planning methods because they want to consider all sorts of options for them to achieve; they are less concerned with formulating a methodical plan since they want to get a feel for the different methods and adopt the one that seems most enjoyable/satisfactory for them to achieve their happiness. Achieving personal happiness is EQUALLY IMPORTANT for the Te and Fi user; HOW to achieve personal happiness is what actually differs.
As for the dom/aux Ti and Fe-users, I think the same distinction would apply-- Fe users are more like Te users in their pursuit of happiness, more methodical and orderly with how to achieve their happiness, except they take into account how others around them would feel about their strategies; Ti users are more like Fi users and more open to the methods they use, except they are more likely to use reasoning, rather than what makes them happy, to adopt one of the many options to achieve what makes them happy in the end. So in the end, achieving personal happiness is equally valuable for all users, regardless of whether Te, Fi, Fe, or Ti is their dom/aux function. What differs based on these functions is HOW personal happiness is achieved.