Asking this question is like asking which computer brand, phone, or even soft drink is better. Everyone has their opinion. My answer to this is that there are times in which each will provide the advantage.
For instance, when printing a large area on a manual, the natural peel of the screen is outside-in; thus a push motion is very efficient to allow the screen to peel away from the substrate as the squeegee passes over the image.
The disadvantage of this action is the fact that the squeegee has become more of a hammer than a subtle tool, so ink flow is limited and can require a second stroke to clear the screen entirely. Halftone images may also suffer from excessive dot gain with this method of print.
When printing simulated process with dark colors on light fabrics and standard sized graphics, I tend to use the pull method. The pull method gives greater control of the pressure being used to clear the screen, along with utilizing the full potential of the squeegee to apply a substantial deposit.
The operator needs to flood the image well to help with this method. The off-contact should be set to allow peel from the inside-out on the press. Printing over large under-based areas are especially sensitive to the peel action.
Either way, the idea is to create a clean print utilizing a proper flood, a controlled print stroke, and an adequate peel. If printers establish these three parameters with the suggested criteria from the ink manufacturer, there is a high chance that the plastisol ink will perform well.
This procedure proves accurate on manual or automatic equipment and is the pathway to clean, consistent quality application.
Knowing the relationship between the fabric, ink, and print will help an operator on any press. The subtle adjustments that will make a print work or transform a good print into a great one are directly related to this parameter. No matter the quality or price of the machine used to print the garments, if an operator becomes a craftsman on-press and makes the changes necessary to achieve this relationship, the final result will be great.
For some thoughts on the ergonomics of pushing or pulling a squeegee, check out this tip.