If you're using a water-retentive medium, the shallower the pot, the more difficult it is to offer your plants a maximized opportunity to realize as much of their genetic potential as possible. The simple reason is, media that hold an excessive amount of water hold too little air, and roots need oxygen as much as they need water in order to function efficiently.
Not all grow media will support a perched water table (PWT), but most commercially prepared media do. Once the particle size is uniformly above 1/10", the PWT disappears. One thing that's good to know is, for any medium that supports a PWT, the maximum ht of that PWT is a constant, and it doesn't matter what the size or shape the container is.
The image below illustrates a PWT of a fixed ht in containers of 3 different hts. See why the shallow pot is more difficult to grow in. If you're using a grow medium that supports 4" of perched water (that's about average) and the pot is 6" deep, the bottom 67% of the soil column will be 100% saturated after a thorough watering. Using the same medium in a 4" deep pot means the entire soil column will be saturated, 100%, but using a 12" deep pot, only the bottom 33% of the soil will be saturated, making the taller pot far more forgiving.
By the images below, you can see that tipping a pot after watering (compare B to A) can significantly reduce the volume of water the pot can hold, and choosing a larger pot in order to make judicious use of ballast (the overturned pot in D is one way to passively use ballast to reduce water retention) can be a game changer, too.
Al