There is no way to compare. However may show that the two results may be equivalent, what differs is the methodology

It depends on your research question. In High/Low Clustering(Getis-Ord General G) we can measure the concentration of high or low values for a given study area. If you want to know are the values and distances are correlated, it probably is a good idea to use Spatial Autocorrelation tool.

The assumptions behind both stats are that your data is continuous (real numbers) and normally distributed in the study area.

If your research question is about measuring the similarity of nearby features you should use Moran's I. The measure only indicates that similar values occur together. It does not indicate whether any cluster is composed of high or low values.

General G statistic can be used to indicate whether high or low values are concentrated over the study area.

Hence, if you wish to find out whether your data is clustered in general (auto correlated) use Moran's I. If you want to know more specifically whether or not there are clusters of high/low values use G stat.

The answer above is great. 

One more tip: it might be a good idea to use both indicators, global and local at the same time (easy to implement in e.g. GeoDa). 

1. Moran's I positive and G positive: high value observations tend to cluster together and their neighbors are similar (high as well)

2. Moran's I positive but G negative: low value observations tend to cluster together and their neighbors are similar (low as well)

3. Moran's I negative and G negative: low value observations tend to cluster together but their neighbors are dissimilar (high)

4. Moran's I negative but G positive: high value observations tend to cluster together but their neighbors are dissimilar (low)

Some additional points that might help:

I hope that adds something to your question and to the other excellent answers!

Cheers, René

Thank you Rene for the usefull answer.

A nice answer can be found here: https://www.mattpeeples.net/modules/LISA.html#:~:text=Moran's%20I%20is%20large%20and,low%20values%20cluster%20in%20space.