What's the difference? Are they really different, with a nuance, or is it just a matter of preference? Does one point to your level of fluency more than the other?
Made up examples.
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"I just want to say that for all the experience she claims she's had, she is not all that competent."
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"I want to just say that for all…"
Would the position of just set the tone for what the speaker is about to say? In "I just want to say…" the speaker might be about to make a comment directed at another comment made earlier or someone and perhaps oppose it or critique it . In "I want to just say…" on the other hand, the speaker may be wanting to add a piece of information, which would keep the tone more neutral.
Best Answer
Most likely, there wouldn't be any perceived difference between the two sentences.
However, there is a subtle difference in interpretation that could be made:
This means that the only thing you want to do is say X. You don't want to run, jump, watch TV, or have dinner. All you want to do is say X.
This means that the only thing you want to say is X. You don't want to say anything else. (However, you might also want to run, jump, watch TV, or have dinner.)
Such a distinction would generally not be made. However, since a difference was asked for, that would be the only subtle one I could think of.
Generally speaking, both I just want to say and I want to just say are the equivalent of let me say or I want to say. They are just general introductions to you making a statement about something. The word just, barring the really subtle distinction I made, could be dropped altogether.