I agree with FreeTrade, why use a memory intensive algorithm for BirthdayHash if you're gonna fill up your ram with hashes anyway?
But either way, here is why it is worse than scrypt:
Your proposed algorithm (momentum) scales super-linearly with the number of computers that can be dedicated to solving the proof-of-work. Set up N computers storing generated hashes in a distributed hash table between them. They now have N times the memory capacity of a single computer and will fill up their memory just as fast. This could scale to pretty large N's, you don't need low latency, you could accumulate hashes on each computer and send them in batches.
And this is bad of course (would lead to centralization).
Suggested modification:
Embrace this and encourage every single miner to be part of the same DHT (Not that simple, but you get the picture), share reward between the computer generating the hash and the one that had it stored. Could work on the current P2P system already in place.
I had considered the potential for such a design. DHT will not perform well enough, you would need 100BT ethernet or perhaps gigabit before the hash table could be filled quickly enough. From what I can tell a SUPER COMPUTER with a ton of RAM and high-speed interconnects would give you the best performance. Here is the difference, such a super computer could be built from commodity parts.
So the question becomes how would such a super computer compete with say a corporate office that works together via the high-speed local network to mine at night? The other question becomes, if you are going to build a SUPER COMPUTER to perform this mining computation then you probably have a dual-use machine that could be used for all kinds of research. This is far better than Scrypt or SHA256.