There are differences in the loot table files for ominous vaults between Bedrock Edition and Java Edition.

The exact loot table for ominous vaults in Bedrock Edition can be found by going to https://github.com/Mojang/bedrock-samples/releases and navigating to "behavior_pack/loot_tables/chests/trial_chambers/", with the relevant loot table files being reward_ominous.json, reward_ominous_common.json, reward_ominous_rare.json, and reward_ominous_unique.json.

The exact loot table for ominous vaults in Java Edition can be found by opening the game JAR file (using a third-party program to open archive files) and navigating to "data/minecraft/datapacks/update_1_21/data/minecraft/loot_tables/chests/trial_chambers/", with the relevant loot table files being reward_ominous.json, reward_ominous_common.json, reward_ominous_rare.json, and reward_ominous_unique.json.

These are the exact differences:

reward_ominous.json:

• In Bedrock Edition, the first pool has a 80% chance to pick reward_ominous_common and a 20% chance to pick reward_ominous_rare.
  • In Java Edition, the first pool instead has a 80% chance to pick reward_ominous_rare and a 20% chance to pick reward_ominous_common.
• In Bedrock Edition, the third pool has a 25% random chance of being rolled.
  • In Java Edition, the third pool instead has a 75% random chance of being rolled. (fixed in 1.21.0.23)

reward_ominous_common.json:

• The loot tables are slightly different between Bedrock and Java Edition:
  • Bedrock Edition:
    • 4 to 10 emeralds, weight 5
    • 8 to 12 wind charges, weight 4
    • 4 to 12 arrows of slow falling (extended), weight 3
    • 2 to 3 diamonds, weight 2
    • 1 ominous bottle, level III-V, weight 1
  • Java Edition:
    • 4 to 10 emeralds, weight 5
    • 8 to 12 wind charges, weight 4
    • 4 to 12 arrows of slowness IV, weight 3
    • 2 to 3 diamonds, weight 2
    • 1 ominous bottle, level III-V, weight 1
      (MCPE-180963) (fixed in 1.21.0.26)

reward_ominous_rare_json:

• The 2nd last entry contains an enchanted book with the Wind Burst enchantment, with weight 1. However, on Bedrock Edition, the "max" field of the enchant_book_for_trading function is set to 1, when Wind Burst can go up to level III. On Java Edition, any level of Wind Burst can be selected. (no longer a difference as of Java Edition snapshot 24w18a, as only Wind Burst level I can be acquired from ominous vaults in there too.)

reward_rare_ominous.json (Bedrock) / reward_ominous_rare.json (Java):

• The loot tables are completely different between Bedrock and Java Edition:
  • Bedrock Edition:
    • 1 golden carrot, weight 3
    • 1 golden chestplate, enchanted from level 5-15 (including treasure enchantments), weight 3
    • 1 golden axe, enchanted from level 5-15 (including treasure enchantments), weight 3
    • 1 block of iron, weight 2
    • 1 crossbow, enchanted from level 5-20 (including treasure enchantments), weight 2
    • 1 diamond axe, enchanted from level 10-20 (including treasure enchantments), weight 2
    • 1 diamond chestplate, enchanted from level 10-20 (including treasure enchantments), weight 2
    • 1 golden apple, weight 2
    • 1 enchanted book, with Knockback I-V, Punch I-V, Smite I-V, Looting I-III, or Multishot I, weight 2
    • 5% chance (with random_chance) of 1 block of diamond, weight 1
  • Java Edition:
    • 1 block of emerald, weight 6
    • 1 block of iron, weight 4
    • 1 crossbow, enchanted from level 5-20 (including treasure enchantments), weight 4
    • 1 golden apple, weight 4
    • 1 diamond axe, enchanted from level 10-20 (including treasure enchantments), weight 3
    • 1 diamond chestplate, enchanted from level 10-20 (including treasure enchantments), weight 3
    • 1 enchanted book, with any level of Knockback, Punch, Smite, Looting, or Multishot, weight 2
    • 1 enchanted book, with any level of Breach or Density, weight 2
    • 1 enchanted book, with any level of Wind Burst, weight 1
    • 1 block of diamond, weight 1 (fixed in 1.21.0.23)

reward_unique_ominous.json (Bedrock) / reward_ominous_unique.json (Java):

• In Bedrock Edition, the loot table gives 1 totem of undying, with weight 2.
  • In Java Edition, the loot table instead does not give this. (fixed in 1.21.0.23)

Attached screenshots show some of the differences in loot, such as different items being given.