I have enough data now to discern a pattern for all possible rune types. Table below shows the multiplier you gain by taking a rune from minimum to maximum level. In the case of Rare and below, that is from Level 1 to Level 20. For Heroic and Legendary it is from Level 1 to Level 30. This data should be helpful for you when deciding whether to upgrade a Rune or not. You can estimate the ending stats that your upgraded rune will have and you can compare them to existing runes that you potentially might swap them in for.
Some interesting things to note. The Tier of the rune didn't appear to matter. The data was the same for Improved, Greater and Superior runes. I didn't have many Lesser runes in my data, but for the few I did have the data was consistent for them as well. Also, the Star level didn't matter. The multipliers were the same at all Star levels. Also, the multipliers were the same for both the primary and secondary stats.
For all the integer based stats (Defense, Health, Attack, Skill), the multipliers are roughly the same between Rare and Heroic, but there is a big drop in the multiplier for Legendary. For example, if you take a Rare rune from Level 1 to Level 20, your Attack rating will double (multiplier of 2.0). If you take a Legendary rune from Level 1 to Level 30, your Attack rating will only increase by a factor of 1.7.
For the percentage based stats (Crit, Damage, Dodge, Damage Reduction and Resists), the multipliers for Heroic and Legendary are significantly higher than Rare runes. For example, if you take a Rare rune from Level 1 to Level 20, your Crit rating will increase by a factor of 2.6. If you take a Legendary rune from Level 1 to Level 30, your Crit rating will increase by a factor of 3.4.
Another interesting thing to note is that Dodge on Rare runes is the worst stat in terms of multiplier compared to all other stats. I'm not sure why they chose to penalize Dodge. Another inconsistency is why the integer based stats on Heroic runes don't get an improvement over Rare runes, while the percentage based stats on Heroic runes do. On integer based stat runes, Heroic and Rares are equivalent, but on percentage based stat runes, Heroic and Legendaries are equivalent.
can provide some insight into this, although they haven't chosen to shed any light on these sorts of questions in the past, so I'm not holding my breath. It would be nice if they would at least check with the devs to make sure these inconsistencies are not bugs and are indeed intended. I'm also wanting to know if the cost to upgrade being the same at all Rune tiers is planned or also a bug. Seems like a Lesser rune should be cheaper to upgrade than a Superior one, but for now they are exactly the same cost.