Te-Ni vs Ni-Te

Before we start, I'd like to shortly summarize these functions first.

Extraverted Thinking (Te) "Depends on external/empirical facts and judges based on the collective truth"

Introverted Intuition (Ni) "Attempts to fathom internal events by relating them to universal psychological processes or to other archetypal images."

Te-Ni: Sets up facts, goals, data and assessments and align it with their subjective symbolic perception. It mainly judges the world based on tangible and concrete facts and assessments and then get backed up by their own abstract, personal theory. It mainly needs the reassurance of its own theories and vision to see if the facts match up/or connect. In other words, Te-Ni mainly puts Te first, and then checks if it corresponds to their own personal symbolic perception. Te-Ni is more decisive and rational, it mainly rules judgements and judges information using objective facts (First) however perceiving things as symbolic and with a sense of abstraction (Second).

Ni-Te: Builds a set of personal theories, visions and perceptions of reality and then see if it facts, data and concrete evidences back it up and support it. It must need facts and external frameworks to back up and support its personal theory and perception of the world around them. They must need tangible evidences to further support their symbolic theory and goals before they take action on accomplish the objective. In other words, Ni-Te mainly puts Ni first, and then uses Te to back up their theory. Ni-Te is more perceptive and observant, it perceives using subjective symbolic imagery (First) then judges information using measurable empirical facts (Second). 

Compare and Contrast: Both need each other to accomplish their said vision or objective, the difference is that Te-Ni judges the world first and then aligns it to their personal abstract perception of the world, whilst Ni-Te perceives the world first and then backs up their subjective perception with Te.