So, it's been a while hasn't it? We still need to wait for the abilities revision of Neptunia, but since I just finished covering Re;Birth 3 and writing a blog for Futari wa, I thought I'd come back to this thread and try to break things down individually.
Power Ups:
Yellow Heart:
Starting with Yellow Heart, how much of an increase her Powered Up form/machinery is
stated differentlly between the original Victory and Re;Birth 3. between the original Victory and Re;Birth 3. In Victory, it is stated to give her power far greater than that of a regular CPU while Re;Birth 3 states it
10x that of a regular CPU. Normally, I would be inclined to discard the 10x as sometimes that is given to instances where it is just stated to be far stronger (see Luffy's Gear Four), but Re;Birth 3 is a much better translation than Victory so I believe 10x is correct.
Though I'm going with 10x, I do feel that giving context to her fights with the other CPUs will help. Its possible that in the game itself her powered up state was already making her base HDD stronger as during her first fight with the CPUs, she seemed to be losing (and she did call them strong), but Neptune states that she is unaffected after taking so many hits. Later, when the CPUs destroy the machine that was powering her and when they were weaker due to having less shares, they were able to easily beat her.
The CPUs also go from getting practically one shotted by Powered Up Yellow Heart's AOE attack (which tired her out) to beating a
stronger, more focused Powered Up Yellow Heart when they had less shares than their first fight (which to be fair is a reoccurring thing in the Neptunia series; see the Killachine fights in mk2 and the Lord Momus fight in Re:Birth).
Cure Black:
For Cure Black, she has the Sparkle Bracelet. For more details about its scaling, I recommend
my blog about it. To try and sum it up here, the Sparkle Bracelets scale above the Rainbow Bracelets and likely the amped Rainbow Bracelets. The regular Rainbow Bracelets allowed the Cures to scale above the Prism Stone enhanced fusion of the Three Seeds of Darkness who were each around the same strength and were stronger than the Cures by a bit (or more than a bit based on the last fight before they became enhanced by the Prism Stones). For the scaling chain of the Rainbow Bracelets:
Base Cures<=Two Seeds of Darkness<Three Seeds of Darkness<<Queen Of Light<=Dark King<<Prism Stone Enhanced Seeds of Darkness<Majin< Rainbow Bracelets
Conclusion and Speed:
Given all of this, I believe that the Sparkle Bracelets are a stronger power up than Yellow Heart's Powered Up State. Also, the Sparkle Bracelets increase applies to both strength and speed while for the Neptunia franchise, power ups/increases in power usually focus on strength with only marginal increases to speed (and given the third fight against the CPUs, that is the case for Yellow Heart). So even if the increases in strength are similar, Yellow Heart would not be able to touch Black.