I have all 3 -
Battle 3 40 orange sponge
Battle 2 Prov 40 blue sponge
Bloom Power purple sponge
Battle 3 is junk - not for high level play - no spin no power - hollow feeling. It is hyped up by people who can not use hard Chinese rubber due to deficiencies in their technique and power. For them Battle 3 is easier to use than Battle 2 provincial.
Battle 2 Prov is the most suited for high level play out of these 3. The sponge in the Battle 2 provincial is much denser than Battle 3 and has great power and spin - even more than H3 National. There is weight in the ball from the Battle 2. The throw is medium to low.
My favourite is Bloom Power. The spin, the power, the price! And it does not need boosting. It's the best Chinese rubber for me. May be it is lacking in power a bit far from the table but it is fantastic close to the table.
I regularly train and play against an rpb penhold player who uses bloom power on FH... The spin -AND spin variation it offers is very very high and reminds me of Adidas p7
It's not bouncy, so serve, receive, touch shots are all amazing - yet as soon a you go 70% + power it's really fast and deadly. In this respect it outshines many ESN which are too bouncy to really play a tight touch / short game.
On blocks, the angle has to be closed because it's a very spinny rubber so it does react to topspin. On counters it's amazing because it doesn't react much and it can borrow your opponents speed and spit it back!
I find it absolutely great on the avalox P500 because it has flex and speed. I think bloom power should be played on slightly Flexi blades with high control to make it shine.
Far from the table it's possible to play, a bit harder than a Tenergy but with good technique it can be played. I think you'd want to go back to medium/ short distance asap though as this is where the rubber is actually better than ESN/ Tenergy