For a majority of weapons, a level 10 4* version will entirely beat out a level 1 5* version, having both two units of CTR and better damage anyways.

There are a few weapons (notably most bombs) which receive non-damage bonuses, which leaves the question of: which ones, and which differences are big enough to be worth the loss of damage and CTR to a player with few radiants?

In my particular case, I almost always run dual Chaos, and often a weapon focus sprite perk as appropriate, making the loss of CTR relatively much smaller than otherwise.

I'm currently planning on upgrading my 4* Freeze Bomb to 5*, in particular for use in Vanaduke runs but also otherwise.
I'm planning on making three alchemers; one freeze, one non-status elemental, and one shadow. Which of those would be at least competitive as 5*? I'm definitely planning on upgrading one, for reasons unrelated to effectiveness, so that's a thing.