For us - there is no debate on wether to prune or not to prune indeterminate tomato plants in a GH. We have grown these plants from pruning as the photos show - to not pruning at all - to somewhere in-between. We have no doubt that pruning the suckers similar to the photos has produced the best results for us!

I decided to strip a tomato plant bare-naked from foliage and tomatoes to illustrate what pruning suckers looks like on a mature tomato plant. The main branches are tied to the cattle panel so the tomato plant lays vertically flat to the panel. I used the "pano" feature on my camera phone to take the photos so they are distorted just a bit - but hope you see the concept. Keep in mind that each plant is not pruned perfect and is adjacent to another plant so modifications are sometimes needed.

Her is a close-up photo of the upper part of a quarter of the total plant - the other 3/4s look similar:

Pruning this method has produced results like this year after year for us!!

I have always said this and say it again, that I make a distinction between a "BRANCHING" and "SUCKERING".
As seen in Hudson's stripped plant ; the main making a "Y". Then each of those make "Y". At the third stage of "Y"ing you end up with 8 branches. But along the way there will be some sub-branching or suckerings from the lower nodes. Those are the ones that I personally won't allow to exist.

As for pruning plants outside that depends on whether someone is staking or trellising or growing them on hogwire, or in cages or just letting them sprawl.

I grew mine by sprawling and some in cages and sometimes the same variety was grown both ways and never once did I take off lateral branches.

The word sucker came about b'c ages ago some felt that leaving them on sucked energy from the plant. But that's not true at all, but the word sucker is still used. Lateral branches are very productive as to fruits, and takingoff those lateral branches just lessens the yield of plants.

Carolyn

Below is a picture depicting part of a bed (~ early August). As you can see, the lower parts are well trimmed/pruned. Even with all that, later in the season the tops got quite heavy.

I will take new pictures and post them.