The original model gives me an AIC of 75.43 and the Box-Cox transformed model gives me -189.2013. Does this me the Box-Cox transformed model is a much better model here?
Generally speaking: Yes, you can compare negative and positive values of AIC, it can happen. There is no reason why AIC should be exclusively non-negative; this has been covered already by some posts here and here.
Having said that, you should not compare AIC values from models with different response values. In that case the (log-) likelihoods calculated correspond to variables from different scales so their comparison can be totally misleading; I discuss this a bit with a bit more detail here.