I think the truth lies somewhere between your two viewpoints. We do have a small squad but Moyes doesn't even utilise that to it's fullest, so lack of numbers can't be the problem.
Mucha has played twice for us this year. Whereas Arsenal's second-choice 'keeper has made 13 appearances and their third choice has played twice. Spurs have split goalkeeping duties between Lloris (22) and Friedel (15).
Our shadow defence have started 23 games in all competitions: Hibbert (4), Heitinga (16), Duffy (0) and Oviedo (3). Arsenal (44): Jenkinson (18), Koscielney (18), Djourou (2), Santos (6) and Spurs (53): Kaboul (1), Gallas (18), Dawson (16), Naughton (18).
In midfield: Everton (7): Barkley (0), Hitzlsperger (4), Junior (1), Gueye (2). Arsenal (44): Diaby (13), Rosicky (3), Ramsey (17), Coquelin (11). Spurs (55): Huddlestone (12), Sigurdsson (12), Livermore (5), Sandro (26).
Up front: Everton (14): Naismith (14), Vellios (0). Arsenal (33): Gervinho (16), Oxlade-Chamberlain (17). Spurs (41): Adebayor (15), Dempsey (26)
There will always be mitigating factors such as our rivals playing in European competition, fielding weakened sides in the League Cup or injuries but, even so, their squad players get much more game time. You could argue that they have greater strength in depth but they're still weakening their first XI by Gervinho in for Podolski or Huddlestone for Parker. And their games are more high pressure because the expectation of Champions League qualification is greater on them.
Heitinga and Naismith are the only two squad men to have started more than 5 games for us this season compared to virtually all of the shadow sides for Arsenal and Tottenham. I appreciate that we have a few youngsters but the North London sides haven't been afraid to use Jenkinson, Naughton, Coquelin, Livermore and Oxlade-Chamberlain. Hitzlsperger is no world-beater admittedly but, if he can't get games ahead of Neville when Gibson is injured then he really is a last resort. Same with Oviedo. Will he only ever start if Baines or Pienaar are unavailable?