I tried S15, one of the more recent Slack based puppies after using various puppies for 15 years now, and honestly I was pretty shocked to realize that slackware has very little to offer in the compiled applications department.
I soon realized that maybe the Slack philosophy is to compile your own programs. And I simply did not want to take that approach.
Pentium4 is pretty old, but fossapup64_9.5 will probably run on it, and it's possible that F96_CE4 will run on it also. I run F96 on all kinds of dual core and single core processors. One is a netbook with 2GB of ram and a single 1.6Ghz cpu. F96 has everything you'd expect from an OS, pulseaudio volume control, easy to connect wifi, etc. Fossapup64_9.5 has more legacy utilities like retrovol, and older puppy wifi network utilities that are not nearly as convenient.
You had a bad experience with a Slack based puppy. There are a whole lot of different approaches to puppy-linux, which if you invest the time in exploring and don't mind a certain learning curve involved, have the potential to give you complete control and versatility when it comes to installing and using operating systems.
What I mean, is that with these OS's it's possible to have a hundred fully functioning and versatile OS's on a single partition, and these OS's once you personally configure them to your tastes can be copied and booted from just about anywhere., backed up and rolled back if you happen to break something by fiddling around.
These are the only OS's I've used for the past 5 years, and I spend about 6 or 8 hours a day doing business/pro-audio work on them. I tweak my OS to my tastes and copy it to the various machines I use at different locations, which are all used 5-20 year old laptops.
If AntiX gives you that kind of flexibility and power by all means use it, but I believe there's a lot more capability available in the OS's available here.