As to the original question of a cartoon depiction of republicans and democrats,
Imagine a big, heavy balloon (of the kind you ride at state fairs) labeled "Government."
The democrat is pumping up the balloon.
The republican is running around with pins putting holes in the balloon.
To me there are several differences between the two that are functionally significant.
Democrats don't believe people know how to take care of themselves, so will try to take care of them - via welfare, social security, medicare, and lots of agencies to review, oversee, direct, and otherwise control private activity.
Republicans believe that market forces are self-regulating and don't need that kind of oversight.
Both are, of course, wrong - because there is a balance point to be had for regulatory agencies. When you continually cut budgets from agencies and then cut the budgets of the watchdog agencies that watch the other agencies, things like the Wall Street debacle and the BP oil spill occur.
Next difference: Entitlement vs. Opportunity - clearly a democrat vs. republican situation. Democrats want to entitle you so they can put you in their back pocket come voting time. Republicans prefer to spend that money on non-social issues. We need balance because spending does help put money into circulation. Saved money does nobody any good once the amount saved gets big enough.
Next difference: Civil rights vs. Moral Majority. Generally a democrat vs. republican thing. Again, we need that balance. GWB cut back on some rights, citing security concerns. Obama wants to grant rights to gays. GWB was not the sharpest tack in the drawer when it came to rights.
Heck, we could go on for a while on the dichotomies. The final difference between them is a matter of style, not particularly substance. Both spend money. More money than we have. The USA taxpayer actually needs to form a revolt and take back some of that money. Mark Twain said it: Nobody's life, liberty, or property are safe while the legislature is in session.