Running python script on external hard disk (training neural network)
It depends on the read speed of your Hard drive and External hard drive.
Is your hard drive a SSD? If it is, then It sure gonna be way faster than your external hard drive.
If the read speed of your hard disk drive and external is same or similar, then its doesn't matter where you store your dataset.
1) Your python file will be "loaded" into RAM, and executed. So your internal hard disk plays no major role.
2)Again, if your External HDD and internal HDD has similar read speed, then it doesn't matter.
I have a dataset that is too large to store locally and I want to train a neural network.
Which would be faster? or are they the same? 
1) All files are stored on the external hard drive. The python file is run in the directory of the hard drive that loads the data and trains the network
2) Python files are saved locally and the loading of the dataset during training is done by pointing it to the dataset on the external hard drive 
I'd assume that the execution speed and loading of the dataset will be equal in both these cases, but I'm not sure