From what I understand, you expect the following result for the given example arrays:

[
    { "account":  4, "balance": 999     },
    { "account":  5, "balance": 999.999 },
    { "account":  6, "balance": 999     },
    { "account": 15, "balance": 999.999 }
]

...as these occur in both arrays.

To achieve that with a better time complexity, use a unique key for each object. Knowing that your objects have a key that consists of two properties, you can combine those two values in an array and produce its JSON encoding (or any other suitable encoding): that string will be a unique id for each object. Store those of the first array in a set, and then iterate the second array to check if the object has such an identifier that occurs in the set.

let currentArray = [
  {account: 1, balance: 200},
  {account: 2, balance: 100},
  {account: 3, balance: 300},
  {account: 4, balance: 999},
  {account: 5, balance: 999.999},
  {account: 6, balance: 999},
  {account: 15, balance: 999.999},
  {account: 8, balance: 100},
  {account: 9, balance: 300},
  {account: 10, balance: 300},
];

let testArray = [
  {account: 4, balance: 999},
  {account: 5, balance: 999.999},
  {account: 6, balance: 999},
  {account: 7, balance: 999.999},
  {account: 8, balance: 999},
  {account: 9, balance: 999.999},
  {account: 10, balance: 999},
  {account: 11, balance: 999.999},
  {account: 12, balance: 999},
  {account: 13, balance: 999.999},
  {account: 14, balance: 999},
  {account: 15, balance: 999.999},
];

const hash = ({account, balance}) => JSON.stringify([account, balance]);

let ref = new Set(currentArray.map(hash));
let result = testArray.filter(obj => ref.has(hash(obj)));
console.log(result);

If you are only interested whether there is such an object, then use some instead of filter. The return value will be a boolean: true when there is such an object, and false otherwise.

If you are interested to find one such object, then use find instead of filter. The return value will be the first found object, or undefined when there is no such object.

The key to the better time complexity is the use of the Set. It could also be a plain object with the JSON strings as property names, and for each an arbitrary value (like true).