I'll take a stab at this but first a couple of comments:
"The more stats, the more complex and
detailed your character becomes.
If you mean complex and detailed in the sense that you've got more numbers in flight, sure. If you mean complex in terms of "Hey, my character is a nuanced being with a unique story!", eh. This especially falls short when dealing with min-maxing... if there are dozens of stats, but only one really useful combination, all you've done is put the annoyance of looking up the optimal build into your players' gameplay experience. You can have perfectly detailed characters (detailed in their interactions with the world) without a lot of stats--see Munchkin, S.T.A.L.K.E.R., or System Shock 2 (granted, that last does have a bit of a skill system involved).
But also, a character with a high Str
typically also has high Con, Defenses,
Hit Points/Health. Without high
numbers in all those other stats, they
might as well not be strong since they
wouldn't hold up well in hand-to-hand
combat. So things like that force
trade-offs within the category of
So, the distressing thing here is that you are assuming a playstyle where people are trying to actually have 'optimal' complimentary attribute loadouts. Why should a person not dump Con to get that many more points in Strength, or dump Defense to get more Health? What's wrong with letting people make glass-cannon characters? Obviously, not everyone will do this--but the option shouldn't be removed.
Now, as to your questions:
What are some pitfalls with a small stat list and a large amount of descriptive powers?
With a very small stat list you potentially limit what the user can do. The trick here is that, depending on gameplay, this can be avoided.
Dungeon Siege only had four stats, if I remember correctly: melee, archery, magic, and max health. These each incremented over time as the player used them, and each had a clear effect on gameplay. This system was a success, because while there were few stats each one completely governed some important aspect of gameplay.
Having secondary powers, or skills as D&D or Fallout would call them, is a good way of combining a limited number of stats into a larger number of game-influencing traits. Moreover, any mistakes the players make in allocating attributes is resolved after some gameplay as skill points are assigned.
The problem you face in those two-tiered systems is that anything that causes stat degradation (attribute damage in D&D terms) needs to be propagated forwards into the skills. For a computer, this isn't a big deal, and players will pick up on "Hey, my lockpicking isn't quite up to par today... lemme fix my agility". For a pen/paper game, this means an extra level of bookkeeping, which is annoying at best and error-prone at worse.
Note that a perk/powerup system is a way of patching up any mechanics or effects not covered by a two-tier system. Fallout did this especially well--"Lady Killer" is a perk whose effects are clearly felt, but have absolutely no convenient way of being expressed using the attribute/skill system.
Is this more difficult to port cross-platform (pen&paper, PC) for example?
The biggest issue going to pen/paper is that the more numbers you have the slower gameplay goes. Character creation goes from being a quick "roll numbers, start playing" to a "roll numbers/calculate armor class/frob spreadsheet" affair. Remember, computers are really good at crunching numbers. Every addition/multiplication you add to a pen/paper game adds delay to the player's actions, whether at creation or during game. This is pretty much unforgivable, and it's why every D&D group I've ever been with uses a strict subset of all of the calculations exposed by the game books.
Which brings us to...
Are there examples of this being done well/poorly?
So, as I already mentioned, Dungeon Siege is a really good example of a game that gets away with having very few stats.
Deus Ex had something on the order of ten skills/stats, each one again directly impacting some aspect of gameplay in a clear and obvious fashion. The player still could make useful decisions about their character's path in the game, but the system was simple enough that doing so was not burdensome. Similarly, the augmentation system as well as in-game items helped improve the skills usage yet further or--perhaps even more importantly--helped mitigate any problems the player would've had encountering a situation for which they didn't quite spec skills for.
Fallout does a good job on handling skills, as mentioned above. The big advantage for them was the ability to use a computer, as most of the bookkeeping is hidden from the player unless they look for it, and so minimally impacts the gameplay. This was so much the case, in fact, that they were able to turn the series into a first-person shooter in Fallout 3.
On the other end of the spectrum, you have FATAL. Look it up; it's got more numbers than you could ever need. Ever. I can't imagine this actually being played in a pen/paper setting, and it is so convoluted a system I can barely imagine implementing it in code (or even worse, as data-driving XML).
GURPS and RIFTS have similar issues with somewhat computationally-expensive systems. The sourcebooks are interesting to read, and full of detail, but actually running through a session can be a chore.
Pathfinder, in my opinion, cleaned up a lot of the issues that D&D 3/3.5 had with their skill system and game mechanics. For example, I no longer have to worry about rolling a rogue who is great at ropes but terrible at acrobatics and climbing, or vice versa. Other than deprecating a large variety of increasingly troublesome sourcebooks, Pathfinder's other big win is combining skills so as to give each a clearer influence on gameplay.
- Don't worry about the exact number of stats, as long as they mean something to the player and aid gameplay.
- Don't worry about the exact number of skills, as long as they clearly influence gameplay.
- Do worry about how tedious calculations will become if you intend to make a pen/paper sytem.
- Don't worry about tedious calculations as much if you are writing a system for a computer.
- Two-tiered systems (primary stats, skills/derived stats) have been shown to work well.
- One-tiered systems (skills or stats) have also been shown to work well.
- Most importantly, do what is best for your players, and after that, what is best for your game. Anything else is just stroking your ego as a designer.