Speech recognition: words vs. phonemes
Most modern speech recognition systems are based on Hidden Markov Models. These are probabilistic models that require a previous training. 
So here is simple comparison:  


By using phonemes you have a reduced number of possibilities (around 50 depending on the language), you get a lot of data to train each phoneme model, by combining several models you can have word models. 
By using word models since the beginning, you would need to have thousands of models to train and probably not enough data.


If you are working on a very simple recognition system, with a very limited set of words, for example, recognition of numbers, then maybe you can use words models that don't require HMMs.