580 or 600 flashes (and there's no advantage to the 600, since the higher guide number is only due to the greater head zoom, and with a Better Beamer you'll manually set your zoom between 35-80mm). I recommend the more powerful flash because even though you'd dial back the power with a Beamer (-2 FEC if using E-TTL), with birds you'll want a fast shutter, and faster than Xsync means using the power-robbing HSS.
Also, it helps to get the flash off-axis to avoid steel-eye (red-eye effect). I use a RRS B91-QR bracket (attached to the lens foot) and an FA-QREX2 extender, along with an OC-E3 cord to get the flash elevated.