Interestingly I seem to have an easier time pulling things together when I ramble here a bit and get some "What exactly are you on?" responses, and I have a few ideas I need to get down and out of my head for yet another Neo title, Genetisys.

Basic Idea: Monster battling ala Pokemon. Really, 'nuff said, right? Kinda yea, kinda no. We have two angles here, of which I want to cover the root here and discuss how to take off to the others.
On the one hand, we have monster battling as a storytelling tool, the players duel with cute monsters, but to what end? Eternal glory? The defeat of a rouge organization? The sheer joy of exploration? "Meaningful" philosophy about the nature of fighting/war, what it says about people, right & wrong etc?
The other is just about purely gameist: My Electric type uses the Electric Attack "Shock!"- It gets a 50% bonus to damage for same-type Attack, which is DOUBLED because your Water type is weak to Electric, meaning you're hit for 250 points of damage! I win the championship cup, bragging rights, and those hot cheerleader chicks on the sidelines totally dig me cause I rule!

Nitty-gritty:
Rather gameist/D&D split to the play - GM plots & plans, players are travelers on adventures, regardless of which of the two versions of the above you look at. I anticipate a good bit of rolling involved here, as combat is the core of the genre and battles will normally be quite uncertain. What I've tried to do is pare down the sheer number of rolls, though poor GM influance could increase that.
Stats will measure how many d6 dice a player gets for various actions and checks, with values added for strength of attacks and levels.
The number four seems to work out fairly well using some trial information: To keep things slim, I'm maxing out the number of die-per-stat at 4, which seems to do a good job of breaking down the groups of monsters in current media (Pokemon player guides made wonderful test sources of information). As well, combat between two similar stated & level monsters will resolve in about 3-4 rolls.
As to what gets statted, I see two "objects" here- Handlers, the people training the Monsters, and the Monsters themselves.
Statting out the Handlers is something reletively new to the genre from what I know, in the video games you're represented by a sprite and a few decisions on what you allow the monsters to learn. Here, I'd like to give the Handlers some definition on how they interact in the world. For this, Handlers will have three stats: Tough, Cool, and Smarts. Initially, players will make their character with 5 points, which will allow them to put one in each stat and follow up with an extra in two or put one in each and the last two points in one.
Monsters get a slew of the standad CRPG stats: HP, Speed, Physical Attack & Defense, Elemental Attack & Defense. Each mosnter will also have a pair of Elemental Types, as mentioned earlier. Borrowing a touch from the Pokemon games, limit the number of skills of each monster, meaning less is about WHO you have in your teams and more about WHAT they know for skills and attacks.

Idea here is to maintain a lot of the crunch that makes the monster battling games so much fun, but at the same time reduce handling time for extended battles. In a "story" mode game, theres going to be more focus on interaction than combat, but I don't want combat to take up the bulk of a session. On the other hand, someone playing in a tournament scenario shouldn't be spending 20 minutes on one combat session when thats the focus of the play.
Let me punch up some trial monsters and stat them out, then can run a couple examples by everyone...

I'd almost imagine adapting Sorceror rules for this.  Those cute, cuddly little monsters always seemed like they were hiding something.

lol - I've actually heard of this happening.
My readings on Sorc, though, don't quite match where I want to go.

Yeah, I'm basically kidding.

However, this does bring up a mechanical question.  Do you really need hard and fast skills and stats or would something like "Vulnerable to Electricity - 2d6" and "Wind Gust Blast - 1d4" be suitable?

The only reason I ask is that Pokemon is already very tightly mechanical (specifically, it being a computer rpg), and I wonder if a slightly different take on the concept would be better/worse/indifferent.

I'm trying to fall somewhere in the middle, as I noted a little closer to the D&D style than the freewheeling style I personally am used to.
Generally, a lot of the fun to be had in the Digimon/Pokemon/Whatevermon games is the mechanical crunch, matching your creature and its skills against another in a duel. I've gone through and broken down the math on the formulas for the Pokemon line and found similar equations for other monster games and it is INSANE to what depth they calculate things. One monster raised by fighting Monster A would be weaker than the same monster at the same level fighting Monster B due to a series of stats and values we never even see. Insane.

The Elemental Type higherarchy would be in place here, as *I* would think it leads to a more stable arrangement than one Electric being "Stong against Water d6" and another miss that completely in leu of something else.
I've broken down the formulas and battles as best I can, I feel, while maintaining that crunch.  Attacks are figured: (Attack Stat roll - Defense stat roll) + Attacks Power + Level Bonus. Generally, won't get too complex on anyone. Start tossing in some bonuses or negatives based on the aforementioned types (+ 1/2, - 1/2 damage) and its still not too messy.

Generally, I much prefer a fast & freewheeling system, both as a designer and as a player. Allows me to lay foundations that let other people expand as a desinger or allows me to add to a favorite system, but this requires a little more structure.

Adventuring Hero
Starting Values:
Tough: 1 or 2 (4 max)
Cool: 1 or 2 (4 max)
Smarts: 1 or 2 (4 max)

The Adventuring Hero your average Genome Handler. A young child with a mind full of dreams, the Adventuring Hero knows the basics of their craft with leanings toward one area or another, but always eager to learn.
The Adventuring Hero’s stats will be evenly spread out, raising them evenly. Upon Handler Creation, the Adventuring Hero’s points will be split as evenly as possible, with 2 points in two categories and 1 point in the third.
Affinity: Choice of Breed

Scientist
Starting Values:
Tough: 1 (3 max)
Cool: 1 (3 max)
Smarts: 3 (4 max)

The Scientist is a child-prodigy, more interested in quantifiable research and facts than in anything else. Quite intelligent, the Scientist will know most all there is to know or learn very quickly.
A Scientist’s main focus will be on his or her intelligence, their Smarts. Smarts will receive 3 of the initial 5 points allotted, while the other two stats will each receive one. Upon being able to raise stats, the Scientist will max out their Smarts first before raising the others.
Affinity: Choice of Psionic or Electric Type