I would compare (1+IRR)^12-1 to XIRR, not (1+XIRR)^(1/12)-1.
The primary reason for differences, despite the "regular" frequency ("monthly") is: (1) the annualized IRR compounds monthly, whereas XIRR compounds daily; and (2) XIRR uses actual number of days, which varies from 28 to 31, whereas annualized IRR assumes equal periods.
Nonetheless, in your example, the max (unsigned) magnitude of the difference is less than 0.18%, and the (unsigned) magnitude of the relative error is less than 15/1000. That seems "close enough" to validate the XIRR calculation, IMHO.
I assume that the amounts are cash flows (deposits and withdrawals), not balances. And I assume that the ending balance is zero after the last cash flow in each column.
I prefer to use TWR (TWRR) instead of XIRR. IMHO, that gives a more realistic view of the performance of the porfolio and individual investments. It is also comparable to market indexes. And that is the default method that investment firms use to calculate "rate of return".
However, that does not require that we track more information; specifically, the beginning and ending balances on each date that a cash flow occurs. At least, that's the ideal. IMHO, it is sufficient to work with the beginning and ending monthly balances, which we usually have in brokerage statements.