It is due to American vs. European expiry, American expiry having higher IV due to early assignment risk, supposedly. I don't know exactly how much this impacts the IV of these series in practice; the bid/ask spread for SPX does seem a bit wider (due to contract size and/or popularity with retail, perhaps), and that may overwhelm any minor IV deficit in SPX.
that would be a model error.
The only difference in price between spy and spx should be American vs European and the dividends. However a proper implied volatility model should account for both.