Why should you not just buy the chain with more links? I have the choice of buying a 114 or a 116 link chain for the same price.

Why would I not buy the longer one and shorten it?

In my case my bike previously had 108 links, and assuming that was correct, 114 should be sufficient, but given it may need shortened, is it not worth buying the longer chain just in case?
If your old chain was sized appropriately for your drivetrain, and you're not changing anything, then you're going to shorten the new chain to the length of the old chain (via counting links, or lying the chains on the ground and pinching them together).

Then, you throw the remaining links into your tool box in case of needing them as spares for a repair in the future. Eventually, you have enough spare links in your tool box and you start throwing the spare links away when you get a new chain (or better yet, as Kibbee suggests, donate them to a bike co-op/shop). 

So, it doesn't matter which one you buy in the long run -- the chain just has to be long enough to begin with (unless its a bike which needs a longer chain, like a tandem in which case you need to buy 2 chains and combine them).