From a Gradient Boosted Model, if you get a continuous prediction between 0 and 1, what is the difference in the meaning of this compared to the probability derived from Logistic Regression?
For example, if I had an LR model output .6 for predicting variable Y, and I had a GBM output .7 for predicting variable Y, is there any significance to the higher value?
Both GBM and logistic regression are probabilistic classifiers; this means that the outputs of both models can (and usually are) interpreted as probabilities. So, there is actually no difference in the meaning of their outputs.
is there any significance to the higher value?
"Significance" is not the right term here; in your example, it is simply that GBM makes a different estimation for the class probability of the specific sample (could be higher, lower, or roughly equal). These two algorithms being different, it is only logical that their probability estimations for the same sample can (and usually do) differ.