It is my understanding that the longest blockchain is the one that should be used.
Is "longest" measured by the number of blocks or the number of transactions?
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The longest blockchain is measured by the number of blocks, not the number of transactions. This is because the proof-of-work is linked to the creation of blocks, not transactions.
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Actually it's the sum of the difficulty of all blocks, but that usually doesn't make a difference when comparing different chains. – jnnk Jan 8 '14 at 20:04
The best chain-tip is picked by the total difficulty of its blocks. This usually corresponds to the chain with the most blocks unless the chain-tips differ in difficulty.
