If I were to compare Battle 3 to the set of Battle Max Pro, Battle 2, Hurricane 3, Hurricane 8, Skyline 2 and Skyline 3 I would say it's closest to Hurricane 8 in terms of how it plays overall. But of course there will be differences.
B3 feels more muted which better control, more spin and better counterattacks. Bloom Power has more of a blast but the ball will go all over the place. Bloom Power is affordable and fun to practice with but is not a professional grade rubber.
I have tried H3 Neo 37, H8 37, Big Dipper 38, Bloom Power 45, 47, Pro Dragon Medium/Soft, B3 38, B2 38 (commercial, provincial, national), B1 38.
B2 Soft 37 is the one I would recommend. Durability is good, price ok and boosts well.