Short answer We do think with 'both', and there is evidence to suggest that we need some sort of conscious representation of our thoughts in order to reason about our surroundings. Emotion itself is not enough.
We do think with our emotional reactions, and we also think with words. When we think with emotions, these are our 'instincts' kicking in. We rely on our emotional ('gut') reactions to tell us when something or someone is dangerous, for example. The instinctual drive is certainly a very valuable thing, and it would be awfully hard to survive without it.
Is thinking 'with words' inefficient? Maybe if an emotional reaction was all you needed in that moment. There are situations -- certain social interactions, for example -- that don't necessitate thinking 'with words'.
However, you can't throw out language entirely. The field of artificial intelligence relies on the fact that the brain can think with words (and, thus, consciously reason its way through situations). The idea of Connectionism in artificial intelligence research relies on the idea that mental states are representational, and thus can be used computationally. In fact, 'neural networks' can be viewed as thinking machines, and most (if not all) research done with neural networks relies on the property that they can think with some sort of representation, language or otherwise.
Why would this be important? One idea is that you need language to make 'connections' (or associations) in your brain between abstract objects. This idea is obviously pretty central to connectionism, given its name. With a storehouse of existing connections, you can modify the 'weight' of these connections upon receiving new input (i.e. new information). In non-technical terms, this means that you can learn more advanced topics, change existing beliefs, and use existing definitions to create newer, more complex ones -- all through human reasoning with conscious representations in the form of language. Thus, language allows us to track the progression of a thought long enough to make a conclusion. If you rely on simply the feeling you get when you see, hear, or remember something, it doesn't do much to increase your ability to reason about that thing.
However, since artificial intelligence focuses almost exclusively on cognition and human reasoning, we could probably look at its shortcomings in order to see where non-representational (i.e. unconscious, perhaps 'emotional') reasoning is a more efficient approach. One obvious problem is that machines can't recognize facial expressions or social context. While you and I could probably recognize a crying face without putting much thought into it, a machine would have to reason through a storehouse of representations (in this case, images of faces instead of words) in order to find the one that represents 'crying'. It would then have to compare this face to the face before it to determine how to comfort it. Even then, it would have to reason through a storehouse of 'comforting' sentences...and you get the idea.
You mention that babies learn faster. This is largely due to the fact that babies are more sensitive to novelty in the environment (see: critical period). This has been demonstrated through studies that show that infants will look longer at a novel stimulus than a familiar stimulus . Given that there is less 'familiarity' in the world of a baby, their attention is more easily captured. There is certainly more to it than that, but there isn't a lot of consensus. We do know, however, that a 'critical period' seems to exist. You might be interested in this paper, which spends some time discussing the progress of a young girl who had lived in isolation and thus had not developed a first language until age eleven. Though she made steady progress, the pace at which she acquired language was much, much slower than that of an infant.
Furthermore, you mention that word length may put a damper on the efficiency of your thought processes. Bear in mind that every language is different. If you were reasoning in Chinese, for instance, your words would be much shorter, and you could arguably think more 'thoughts' in less time (the Chinese language lacks inflection, for instance). However, longer words can also provide more room for specificity. Many modern day concepts (the concept of 'intuition', for example) came directly from German, a language notorious for its long words.
 Turk-Browne, Nicholas B., Brian J. Scholl, and Marvin M. Chun. “Babies and Brains: Habituation in Infant Cognition and Functional Neuroimaging.” Frontiers in Human Neuroscience 2 (2008): 16. PMC. Web. 24 Aug. 2015.