Home university with full research funding or prestigious university with teaching / research assistantship?
In general, to be perceived as a hanger-on, a marginal person, at a high-status place is definitely limiting... while being a star and highly appreciated at a lower-status place (while admittedly not as good as being "star at high-status place") is generally perceived as a good thing, with upper bounds as yet unclear. (Here I speak from a U.S. perspective, where things are not as centrally organized/controlled as, e.g., in France or China...)

That is, in the U.S., it is generally understood that, though of course a trajectory that leads directly to high-status situations is the simplest, there are many "second chances". Perhaps this is less so in more overtly and officially hierarchical settings. And, indeed, as things get more crowded in academe, the second chances in the U.S. are fewer and fewer, but they do still exist.

... not to mention the psychological impact of being told daily that you're marginal. Oof. Not helpful. Better to be told daily that you're doing great. Or is that a matter of taste? :)