CNN: Is it better to train 300.000 images during 1 epoch or 300 images during 1000 epoch?
No, they are not the same. 
*The number of examples you show the network defines what it will be looking for - a network with more examples will tend to be more general. If there are, for example, 1000 pictures with different dogs in it, and you only show 300/300000 pictures, the network (on average) will only recognize one specific kind of dog, and be unable to pick out common traits of all dogs.
*An epoch is basically modifying the network in a small step, and the key word here is small - taking too big steps risk overshooting our target values for the network parameters. Since we´re taking small steps, we have to take several of them to get where we want.
This question is related to convolutionals neural networks (especially YoloV3)
Since one epoch is one forward pass and one backward pass of all the training examples, for the model to converge properly, is it the same (in terms of precision and time to converge) to :

train with n*k images during m epochs ?
train with n images during m*k epochs ?