In my opinion, leave one out cross validation is better when you have a small set of training data. In this case, you can't really make 10 folds to make predictions on using the rest of your data to train the model. 

If you have a large amount of training data on the other hand, 10-fold cross validation would be a better bet, because there will be too many iterations for leave one out cross-validation, and considering these many results to tune your hyperparameters might not be such a good idea. 

According to ISL, there is always a bias-variance trade-off between doing leave one out and k fold cross validation. In LOOCV(leave one out CV), you get estimates of test error with lower bias, and higher variance because each training set contains n-1 examples, which means that you are using almost the entire training set in each iteration. This leads to higher variance too, because there is a lot of overlap between training sets, and thus the test error estimates are highly correlated, which means that the mean value of the test error estimate will have higher variance.

The opposite is true with k-fold CV, because there is relatively less overlap between training sets, thus the test error estimates are less correlated, as a result of which the mean test error value won't have as much variance as LOOCV.