As a PC? Neither, because neither is cost effective. You can't even begin the game with the CAST implanted in something, even with Restricted Gear.
In a more general sense, CAST seems the better choice. It's more humane (for those who care), and allows for more choice in augmentation (for those who don't). Even assuming you don't mind the cost (Essence and nuyen) for Stirrup interface, there's a lot of biodrones who won't need it. Spying (one of the best uses for biodrones) isn't something you really need a huge amount of initiative for, and if you're jumped in, the skillwires part of it isn't necessary.
Flavor-wise, the Stirrup implant might give the rigger a more direct feel of what it's like to be the animal too, which is something some characters would look for. Being a drone is pretty badass, but being able to be a wolf or a tiger is pretty damn cool too. Who needs the Shapechange spell?
However, specializing in biodrones is a poor choice. Even the book spells out that they aren't very effective outside of their very small niche, require more upkeep than drones, and elicit a very poor reaction in a lot of people. The last two might not actually come up in your game (as they actually cost less than drones, since they heal naturally, and you might not care what people think) but the first will come up a lot. Mounting a weapon on a biodrone is a lot harder to do; flying biodrones are more fragile than normal drones and basically can't house weaponry. And it's a hell of a lot more expensive to buy augmentations for a biodrone than to buy mods for a normal drone.