If your theory was correct (that Arsenal are simply better at beating the 'poor' teams), then one would therefore assume that Spurs were actually just as good as Arsenal at beating the 'good' teams. Indeed, if your theory also included that Arsenal were better at beating the 'good' teams as well as the 'poor' teams then it's not much of a theory... it would just be that Arsenal are better full stop at winning all games. So if we go on the assumption that your theorizing that Arsenal are only better against the poorer teams, we would expect similar results between Arsenal and Spurs against the 'good' teams. So let's compare our competitive results in all games against Chelsea, City, United and Liverpool this season:
Arsenal P6 W2 D2 L2
Spurs P8 W1 D1 L6
Doesn't look particularly even to me.
Might it just be that there are more teams better than Spurs than there are teams better than Arsenal?