If you don't care about PvP at all and won't participate in it outside of the very occasional group fight, I wouldn't advise picking strength if you also aren't likely to get artefacts. Constitution will have a much larger impact on your ability to hunt harder areas effectively.
If you have any intention of participating in PvP on a (semi-)regular basis then strength is the better choice.
Unless you don't want to do combat ever. Which isn't the case since you're in the Shield.
The reason why it's important is because your win-condition as Runewarden is disembowel. Disembowel deals % health damage proportional to your strength stat. A base of 14, +1 from Improved Physique, +1 from Jera and +2 from Fury puts you at 18, which is usually considered an okay base-strength for this finisher (it deals approximately 92% of your target's health worth of damage). 22 or so is what's required for a guaranteed instant kill (100%), but you'll be doing damage by the nature of your prep, especially as a Two-Hander.
Being able to hit that 18 strength floor with 14 constitution to go with it is insane, trust me, it's the best choice.
Answers
Unless you don't want to do combat ever. Which isn't the case since you're in the Shield.
The reason why it's important is because your win-condition as Runewarden is disembowel. Disembowel deals % health damage proportional to your strength stat. A base of 14, +1 from Improved Physique, +1 from Jera and +2 from Fury puts you at 18, which is usually considered an okay base-strength for this finisher (it deals approximately 92% of your target's health worth of damage). 22 or so is what's required for a guaranteed instant kill (100%), but you'll be doing damage by the nature of your prep, especially as a Two-Hander.
Being able to hit that 18 strength floor with 14 constitution to go with it is insane, trust me, it's the best choice.