This topic has been debated over the years. Bill Munson thought there was no noticeable difference. Hybridizer Don Jerabek has noted some difference on a few of his long crosses. Google Watson Park Daylilies to see his findings. I haven't hybridized long enough to form a personal opinion. My guess is the luck of the genetic draw.

I will do cross the same parents both ways and have not seen much of a difference between the 2 sets of seedlings. They have always almost all looked alike, and every so often one pops out that looks like a step child. I have two sets that come to mind.

AVANTE GUARD X UNKNOWN & UNKNOWN X AVANTE GUARD, all of the resulting seedlings were for the most part yellow to orange in color with stippling, but there is one I call "FLOPPY RED" that is a muddy red with no stippling. There are a couple interesting seedlings that I have kept.

INCHON X SOUTH SEAS & SOUTH SEAS X INCHON, these are all shades of whatever color you want to use to describe SOUTH SEAS. There were some nice seedlings in the group, I kept 2 that I thought had better form than SOUTH SEAS.

On the other hand INCHION X STRAWBERRY CANDY & STRAWBERRY CANDY X INCHION gave me a wide variety of colors. INCHON gives up its color well, and has pretty nice form, which was better in the plants with it as a pod parent.

There vere probably 12 to 18 seedlings in each group, I don't consider that a long cross, but I feel it gave me a good cross section of what they could produce. I only grow out about 6 to 10 of a cross now and if anything interesting pops up I repeat it and grow more. There are some no brainers for example FORESTLAKE RAGGAMUFFIN X almost anything is worth growing as many as you can.

A good thing about the on-line databases such as Tinker's and the AHS is the ability to search for children. For example, search IDA'S MAGIC with roughly 350 children. You can compare foliage habit, flower form and color and maybe more traits for both Pod and Pollen parents. See if the same trends persist when IDA is pod parent versus pollen parent.
There is additional DNA material in the endosperm of the seed which is contributed by the pod parent only, but no one knows for sure what it does, at least not that I'm aware of.
When you consider that the result of a cross may have from 1 to 8 million possible outcomes, you must look at a fairly large number of cases before you could consider any pattern significant. I would say 1000 outcomes would be a decent number.
Ed

Thank you shive & bambi & ed ~ much to ruminate on: 8 million to 1 odds, no brainers & Watson's observations have given me lots to go forward with... ~m'