It may be similar to Vanishing, simpler creatures are easier.
Professor McGonagall explains to her class that how difficult it is to successfully cast a Vanishing Spell depends on the complexity of the creature being Vanished.
“Looking supremely unconcerned, Professor McGonagall addressed the class once more.
‘As I was saying: the Vanishing Spell becomes more difficult with the complexity of the animal to be Vanished. The snail, as an invertebrate, does not present much of a challenge; the mouse, as a mammal, offers a much greater one. This is not, therefore, magic you can accomplish with your mind on your dinner. So – you know the incantation, let me see what you can do …”
- Harry Potter and the Order of the Phoenix, Chapter 15 (The Hogwarts High Inquisitor)
Similarly, it may be easier to conjure simple animals than complicated ones. The flaw with this theory, however, is that snakes and birds aren’t the “simplest” creatures possible. If this was true, then invertebrates like snails should be the easiest to conjure.
There’s nothing that gives reasons that these specific animals are easier.
Serpensortia was only used once by Draco Malfoy in the duel with Harry, and Avis was only used a few times, by Ollivander to test Krum’s wand, and in Transfiguration class as a spell the students were learning (though only Hermione succeeded, and she set the birds to attack Ron). There’s no more detail given on them, nor is it mentioned anywhere why snakes and birds are easiest to conjure. Some animals do “take differently” to magic, though. A writing on Pottermore said pigs are said to be quite un-magical, and difficult to charm. However, it’s never mentioned exactly what about pigs makes them this way.
The most commonly cited signs were: onset of magical ability before the age of three, early (before aged seven) prowess on a broomstick, dislike or fear of pigs and those who tend them (the pig is often considered a particularly non-magical animal and is notoriously difficult to charm), resistance to common childhood illnesses, outstanding physical attractiveness and an aversion to Muggles observable even in the pure-blood baby, which supposedly shows signs of fear and disgust in their presence.
It’s possible that, similar to how pigs are difficult to charm for some reason, that there’s just something about snakes and birds that make them easier to conjure than any other animals.