The main and possibly only difference is language registry.
Presque is standard French.
Limite is normally a substantive that started to be used as an adjective and here is colloquially used as an adverb.
As Stéphane commented, limite can be considered stronger than presque, i.e. closer to the limit, precisely.
In addition to à deux doigts, I would also suggest quasiment and pratiquement.
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