There are a couple of slightly different approaches to the concept of external power packs. Those which plug into the external power port (as opposed to replacing the flash main cells) work by increasing the voltage up to circa 300v. Most flash units capable of this approach have a cut-out which limits the voltage which can be input in this way (the Canon 580EXII, for example, has a protective cut-out at 340v).
The different approaches are:
- Either 6 or 8 AA cells in a single circuit.
- 8 cells in 2 seperate circuits or channels (obviously 4 per channel)
- High power SLA cell.
- High power, industrial size NiMH accumulator(s)
- Design 1 (Canon CP-E4 and Yongnuo SF-17 / SF-18) provides a basic increase in stored capacity up to the sum of the individual cell's capacity. The drawback is that, as a single circuit they are only as good as the weakest cell in the set - it's either all or nothing.
- Design 2 (Pixel TD-381) provides two individual channels. Advantage is that if a single cell is defective, there is still a second channel so you do still get a speed advantage. Because there are ony 4 cells per channel, each channel has reduced capacity compared to Design 1. The combined capacity of both channels is the same as Design 1 and the pack can be used, if necessary, with just one channel if required. Greater flexibility than Design 1 but no major advantage other than that.
- Design 3 (Quantum) is the often best in terms of capacity but suffers the disadvantage of added weight and greater cost. New cells are not as readily available as AAs and may require specialist fitting in due course. They do last a long time though - 10+ years is not uncommon.
- Design 4 (Godox) is, in some respects, a compromise between Design 1 and Design 3. The cell(s) are more readily changeable than Design 3 but considerably more expensive and less readily available than Designs 1 & 2 (not in your local supermarket!). They tend to be lighter than Design 3 but still noticeably heavier than Designs 1 & 2.
Each style of power pack only
supplements the power available for the actual flash, it is still necessary to have cells within the flash unit to power functions like zoom, power setting, ETTL functions, etc. It may not be relevant to your particular use but an external power pack is advantageous if access to the flash unit is limited. If you can't easily get at the flash, say it's up on a balcony or across a busy racetrack, then it's sometimes difficult to simply replace the internal power cells!
My feeling is that
Design 1 only adds minimally to ease of use, with the CP-E4 being particularly pricey for what you gain. The circuitry only requires a single cell out of the 6 or 8 to run down (and there is always 1 which empties first) and the pack just becomes dead weight.
Design 2 has a built-in fail safe so that when 1 cell goes down you do still get the advantage of faster recycling, albeit slightly more slowly than with both channels. In any set of power cells, there is always one which isn't
quite as good as the others and it is that cell which governs the accessibility of the whole circuit.
Design 3 provides arguably the best option with high capacity sealed lead acid cell but the lead acid battery does tend to be relatively heavy (by comparison).
Design 4, in addition to the characteristics previously mentioned, is available in a truly hideous colour if you want to demonstrate excurciating colour perception to your clients (and black too, for the more staid).
Designs 3 & 4 both offer a
major benefit
if you may change flash brands at some future date, they can be updated simply by purchasing an alternate cable. The other designs tend to be brand-specific.
Since retiring 6 years ago, my needs are less demanding than hitherto but I would still opt for Design 2 as the best compromise, especially within your prescribed financial limits. Charging time with any of the designs isn't really a consideration as rapid chargers are readily available for AA cells - but
really fast charging isn't good for any type of accumulator. 2 hours isn't a particularly fast charge for any of the tyoes mentioned here - hence it's not really a consideration. BTW, I find keeping fingernails trimmed obviates any problems getting cells out of chargers.

I currently own four Pixel TD-381s
(and a TD-382 for Nikon) which have proved exceptional value for money. I wouldn't even bother with a CP-E4, personally.