Well the reason I don't like the "egg group" in Pokemon is because each pokemon is a different species and species don't mate with other species in most cases. Some do, but they almost always produce infertile offspring.
Basically the way my monsters are broken (with real world creatures) down are...
Kingdom (Animal) -> Family (Feline) -> Species (Lion)
Kingdom (Animal) -> Family (Feline) -> Species (Tiger)
Kingdom (Animal) -> Family (Canine) -> Species (Wolf)
Kingdom (Animal) -> Family (Canine) -> Species (Fox)
A Lion and Tiger can Mate, but a Wolf and Fox cannot.
Tigers can mate with other tigers, Lions can mate with other Lions, and Wolves can mate with other Wolves, Foxes can mate with other foxes.
And Lions nor Tigers can mate with foxes or wolves.
Pokemon are just crazy even though they do have the above type of categorization to some degree. The egg groups are just all over the place where some species cannot mate with itself. Some Species can mate with other kingdom. etc...
The 1 Kingdom that can mate between all or most of the families/species is Humanoid and that is pretty much following mythology rather than genetics... for fun ^.^
As far as fun goes, I think both have equal merits as to how fun they are. There is definitely something to be said to about merging 2 species together and getting some weird new species, but there is also fun to be had in having constraints placed on what you have to work with to get what you want too.
Considered the you fighting with your pets thing... for me it's a no-go for right now anyways mostly due to I couldn't do it if I wanted to. I've considered the whole multi-pet thing too. The problem there is AI and CPU... if the problem is only AI then I'll do it if I can... if it's CPU it's a no go... another part of the plan is to make this for tablets as well as PCs ^.^ so I want pretty much the minimum happening on the screen as possible. Currently my thinking is Pokemon style of grass = trigger into random battle, but if the CPU load isn't bad I see no reason not to have a set of pets fight freely around you with AI controlling their actions while you issue commands... But for now...small steps ^.^
---------- EDIT -------------
My first attempt at creating an stat gene algorithm thing didn't quite work...
I pretty much made it so that I could set the number of genes on each genome and then randomly generate which attribute and what value...with the value ranging from -3 to 3... and then compare the 2 chromosomes... which resulted in mostly negative stats... So yeah that didn't work
I tried to limit the negative stat genes so that only 1 in 3 times a negative number comes up does it get through... better, but not by much.
Then I removed the negative values so i could only get 0-3... and the results are meh due to some stats not getting any... which sucks and far too uneven.
So the next thing I'm going to do is make it so that each area is handled by 1 chromosomal pair... That should make it so i can get a more controlled distribution of points in the stats in a given area as well as in what area the stats go in. I think I'm also going to limit the number of negative points to maybe no more than 1/3 of the overall genes in a given area, maybe up to half. Maybe I'll take them out as they cause problems all together, but i dunno, depends on if after I finish this it doesn't look right still.