I went ahead and took the survey myself. I answered neutral on whether I prefer the old or new honor system because there are things in both systems that I like and dislike.
Old Honor System Likes:
The continuous loading screen and champion select banners.
The ability to honor multiple people, even on multiple teams.
Viewing how many honors I've gotten in all 4 categories.
There's no time limit on deciding which persons to honor and for what category.
Old Honor System Dislikes:
Lack of clarity with knowing when and how to get certain and particular banners.
Honors ran out quickly if you're like me and tend to honor allot of people on a frequent enough basis.
Banners could replace each other without warning and without notice and with no way to pick a particular banner that you liked to display in games.
New Honor System Likes:
Honors never run out, letting people like me honor people more often without fear of them ever running out.
You know when you can expect to get the special loading screen banners/flairs.
New Honor System Dislikes:
You can only honor one person on a team instead of multiple people on a team.
Lack of clarity of how far along you are in the new Honor levels.
You can accidentally honor an unsportsmanlike player post-game since you're immediately presented with the option to honor someone as soon as the game ends and the post-game lobby begins.
The time limit to honor someone is really poorly planned in my opinion, which can lead to some hasty honor decisions that were not apparent in the old honor system.
So yeah, like I said, there's things about both systems that I l both like and dislike, hence my voting of neutral in the survey itself.