The shorter the rounds (the higher the pool hash rate), the lower the hash rate threshold where you will make more using PPS than Proportional.
The profit doesn't depends on round length at all.
Sure it does. If a low hash rate worker can create only a few shares during a given round, then that means the last share worked on in any given round will likely be discarded due to long polling or be stale when submitted and that last share is proportionately a larger amount of their worker work output. When rounds get short enough on average that a worker can't create many shares in a round, then a significant percentage of a worker's total work [on average] will be wasted when a round ends. With faster hash rates, the amount of work lost to working on a stale share [which LP helps reduce] will be much smaller as a total percentage of all the worker's work. Essentially, it is because a share is a quantum amount of work [you don't get paid for 0.5 shares ... there is no such thing and no way to submit it anyway when the round ends]. It is clear that for PPS to pay better over time, the difference would have to be close to 7% [difference between proportional fees and PPS fees]. That would probably have to be a pretty low hash rate per worker, but as difficulty increases, the number of shares accepted will decrease and this will drive up the threshold.
A scenario that can be easily tested is to run many CPU miners in parallel and such that their cumulative hash rate is the same as a single solid GPU worker. See which one gets paid more using proportional. In a large pool, it will be a notable difference.
If it were possible to submit partial shares when a round ends and not have them be invalid, then the quantum effect would not occur.
A simple example. Suppose that a nice slow worker averages 5 shares during an average round. It should be clear that when a round end, the worker is working on the sixth share on average and never gets paid for that work. So, that would be on average approximately a 10% loss (average share loss would be half a share with long polling working perfectly) and 0.5 / 5 shares accepted is 10%. Clearly, if a miner on average produces several thousand shares in a given round, then the effect is negligible.
To me, that says, low hash rate workers [even if one has dozens of them running parallel] will do better with PPS or using a smaller pool. Like I said, I am not sure what that quantum threshold [my name for it] is, but it should be relatively easy to calculate by the people running their workers [they know that their hash rate is fairly constant per miner and then it is simply a matter of math based on the average number of shares submitted versus the average round length, which is a function of pool hash rate over time].
I am sure this could be explained more easily by somebody less wordy than myself, but I tried anyway.