Base_Transaction_value is the (transaction_cost*transaction_quantity) with the org having functional currency depending on Actual Cost.
Currency_conversion_rate is taken for reporting currency.. like Transaction_value with respect to Transaction cost

execute the following script for some of your transaction_id's for better understanding

    select mmt.transaction_id, mmt.organization_id,mta.reference_account,mmt.costed_flag,
    mmt.actual_cost,mmt.transaction_cost, mmt.transaction_quantity, mmt.new_cost, mmt.currency_conversion_rate,
    mta.transaction_value,mta.base_transaction_value
    from mtl_material_transactions mmt,mtl_transaction_accounts mta
    where mmt.transaction_id = mta.transaction_id
    and mmt.transaction_id = &transaction_id

thanks,

Your answer is a bit confusing but based on what you wrote I interpret Base_Transaction_value to be the transaction value in the currency of the actual acquisition cost (i.e., USD as example) while Transaction_value is the value translated to the ledger currency (i.e., EURO as example).