Codex was a miserable experience for me until I learned to compact after every feature. Now it is a cut above CC, although the latter still has an edge at TODO scaffolding and planning.
I don't even compact, I just start from scratch whenever I get down below 40%, if I can. I've found Codex can get back up to speed pretty well.
I like to have it come up with a detailed plan in a markdown doc, work on a branch, and commit often. Seems not to have any issues getting back on task.
Obviously subjective take based on the work I'm doing, but I found context management to be way worse with Claude Code. In fact I felt like context management was taking up half of my time with CC and hated that. Like I was always worried about it, so it was taking up space in my brain. I never got a chance to play with CC's new 1m context though, so that might be a thing of the past.
/new (codex) or /clear (claude code) are much better than compact after every feature, but of course if there is context you need to retain you should put it (or have the agent put it) in either claude/agents.md or a work log file or some other file.
/compact is helping you by reducing crap in your context but you can go further. And try to watch % context remaining and not go below 50% if possible - learn to choose tasks that don't require an amount of context the models can't handle very well.
Cursor does this automatically, although I wish there was a command for it as well. All AIs start shitting the bed once their context goes above 80% or so.