Rough numbers for halo2 from the Q3 livestream:

These are for a sapling shielded tx:

Groth16

Size 192 bytes 
Verification time: 7-10ms
Proving time: 2s

This is for 2inputs-2outputs

Halo2 - naively implemented

Size 1.5KB
Verification time: 30ms
Proving time: 1 second

This is also for 2inputs-2outputs

Verification is parallisable, so I guess 3 proofs verified in parallel will give you the same speed as Groth16. 3 proofs would equal 3 sapling transactions.

Where the improvements come in is due to the fact that:

1) the circuit is no longer static, so you can create a Xinputs-Youtputs transaction. When you look at the amortised cost of each input, it is better than groth16. So the more inputs you have the better it performs than Groth16, I’m guessing this is up to some overhead.

The information on that part was still a bit ambiguous for me.

2) a different hash function for merkle trees that is 20X more efficient than pedersen hash. He mentions that this haha function can not be efficiently implemented in Groth16, I think he means R1CS here, which is why PLONK is used instead