efficiency: database functions vs. math functions vs. array formula

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I can accomplish the same task using a database function (i.e. dsum), a
math function (i.e. sumif), and an array formula. If my goal is to
make the spreadsheet run as efficiently (fast) as possible, which
should I choose? Let's assume this is a very large set of data, and if
pertinent, the equation will be used frequently.

Also, I've heard array formulas in large volumes can slow down a
spreadsheet considerably. Why is this the case? What is the best
source for finding out information like this?

Thanks for your help.
 
On a related note, how do the three data retrieval options compare:
VLOOKUP with MATCH, DGET, and INDEX?
 

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