The reason why CBC is considered better than ECB has nothing to do with situations involving an attacker with a partial ciphertext; we always assume that any attacker has full access to the ciphertext.
Instead, the problem with ECB is that it leaks information. Specifically, if you encrypt two messages which has two blocks of plaintexts in common, then with ECB mode the corresponding ciphertext blocks will be the same. The attacker can see that, and can immediately deduce the relationship between the plaintext blocks; even if this doesn't give him immediate information about what the plaintext block might be, it tells him something about the plaintext, and that something is more than what we'd like to give him.
This doesn't happen with CBC mode; the previous ciphertext block (or IV) is effectively random (and independent of the plaintext block), and so what is presented to the block cipher is an effectively random string; a collision there is no more likely than it would be if we were encrypting random blocks.
Here is a famous example of this; here is the original image, the image encrypted in ECB mode, and the image encrypted in CBC mode:
As you can see, you can still visually see the image in the ECB mode encryption (it helps that the image is a cartoon, and so there are large areas with the exact same color); you can't see anything in the CBC mode encryption.
Now, if we were encrypting random blocks of data, it turns out ECB mode actually does work out; with random data, you are quite unlikely to run into the exact same block of data twice, and so this 'leaking when two blocks are the same' is not an issue. However, in the real world, we often encrypt things that are quite nonrandom; we need our cryptosystem to be able to deal with it.
