CTR with no authentication is strictly better than EBC with no authentication in that case. Similarly, CTR-then-MAC (with MACs being e.g. per packet) is strictly better than EBC-then-MAC.

Missing (or duplicating) a block in the CTR (counter) block cipher mode messes up the alignment of the count. Then everything after that comes out as random garbage.

CTR is not a very robust block cipher mode...

As long as you simply transmit the count in the packet this is not an issue. You mostly have to do that anyway, because packets can be reordered and you want to stitch them together in order (with holes).

Missing or duplicating a block anywhere in a ciphertext should completely prevent decryption; that's how authenticated encryption works. The idea that some cipher modes are more or less resilient to corruption is, for the most part, a discredited 1990s idea.

In this setup we want to be able to decode a cipherstream with holes into a plainstream with holes. This is very much possible with CTR-MAC, as long as MAC is done on some finitely-sized segments.

That is a problem that is generally handled at a higher level than the block cipher mode.