After talking to @fredley and a few others, I want to ask the community here when and where barrels, chests, and dispensers should be used. What are the pros and cons of each?
Chests can hold a variety of items, and can be accessed with tubes/pipes on every side. With the Iron Chests mod (included in FTB), chests can store many slots worth of items in a single block.
Barrels are single-type storage, but can store 64 stacks of that one item. The item type it can store is set by the first item put in a barrel, whether by hand or by pipes/tubes. Pipes and tubes can connect only to the top and bottom, and further, the top can only be used for input and the bottom only for output. Double right-clicking with a matching item will place all matching items in you inventory into the barrel, making them great for dumping material at lower tiers (before you have sorters set up).
The largest upgraded chest (Diamond) can hold more than a regular barrel, but the upgraded barrel (the Extradimensional barrel) can hold even more than a Diamond chest.
Dispensers are poorer than both in almost every way. They hold fewer item (9 stacks), are as slow to access manually as a chest, require extra devices to access in at one-click speed like barrels, and give random items unless its contents are homogeneous. Their advantages are situational: they're stealthy (accessing manually makes no noise, unlike both chests and barrels); and dispensing with redstone gives a single item instead of a whole stack, which can be preferable. Their greatest advantage will come with the 1.5 update though: dispensed tools and armor will auto-equip.