Is CBC theoretically harder to brute force when compared with ECB? Theoretically – is CBC mode harder to bruteforce when compared with ECB when assuming:


we ignore computational cost for the XOR operations, and
the IV is made public?
As Maarten Bodewes already wrote in a comment, if you ignore the computational overhead of XOR, then there is essentially no difference in CBC and ECB for a bruteforce attack.

However, the question is actually mixing oranges and apples (and it is not obvious), because the security weakness of modes of operation has nothing to do with the underlying symmetric cipher - and a brute force attack has everything to do with the underlying cipher.

The problem is, that brute force attacks are a completely different scenario than what the different modes of operation try to achieve. In brute force you actually try out keys until you find the correct one. In cryptanalysis this is called a total break. The weakness of ECB compared to CBC is, that you can actually can achieve an easier goal of the attack: A distinguishing attack works on ECB and doesn't (with proper randomness, etc.) on CBC - under the assumption that the cipher is secure.

Btw, your 2. assumption is not needed. The IV is always assumed to be publicly known (and generated randomly for security arguments).