I recently asked myself a random question, what would happen if Enervating Mist (handsize down to 5) and Silent Wobby (limit handsize to 3) were active at the same time. Would it just be last or first one (based on activation order)?
From the ruling on Enervating Mist I see the following, emphasis mine:
If "Enervating Mist" and "Infinite Cards" are both active, whichever effect resolved last is dominant.
So yes, it will depend on the order of activation (and thus, order of resolution) which effect takes place.
A related fact is the "negative precedence over positive" rule (as in MTG IIRC). This means that if an effect says that someone can do X, and another effect says that someone cannot do X (they contradict each other), the cannot takes precedence over the can.
This is not the case for the specific cards you mentioned, but is worth mentioning nonetheless.