There are many more factors that need to be considered to make a decision of how or whether to play 44. For example: position, stack size, tournament or cash game, how many players in the hand, how often the blinds increase if in a tournament, etc. A strategy that just says shove or fold is pretty incomplete.
All of these factors have a huge impact on how you play this hand. These are two typical scenarios that you will run across:
1. You're on the button in a 9-handed table in a tournament that has just started and everyone is 100+ BB deep. Regular tournament, so the blinds are increasing slowly. UTG limps and so do three other players. It's crazy to shove here, you can't win the tournament on the first hand but you can sure lose it. Limping in to set-mine is a good option. I don't like raising here with a bunch of players already in the pot because people often like to limp-call and see flops in the beginning, if the flop comes AKJ or something like that then you're most likely beat.
2. You're at the final table in a tournament, down to 4 players, and you're the short stack with only 3BB left. In nearly every case you're going to shove this hand from any position. For me, due to the stack size in a scenario like this I'm usually going to get it in regardless of what else is going on even if everyone else is already all in. You desperately need some chips here because you already have one foot in the grave.