Republicans:
Their would be a welfare system for people who are injured or sick, but healthy able-bodied people would be required to do something in exchange for assistance. The gov't would probably continue to be a huge percentage of the GDP, but 1/2 or more would go to military spending.
Some of the constitution would still have meanings (guns, speech, etc). Judges would not write laws from the bench. Same-sex marriage would probably not be allowed.
Federal Income Tax and the IRS would both still exist... but probably not be as oppressive as they are now.
We would have a HUGE standing army, navy, air-force, marine and space division.
Schools would probably still be federally funded, but there would be an entire year devoted to the greatness of Lincoln and Reagan.
Every aspect of your personal life would probably be monitored and legislated (much as it is today). However, the idea of a "Twinkie Tax" to punish fat people would be laughed out of congress. Smoking cigarettes would probably still be legal, but the federal "sin" taxes would probably be less.
Where you worked would be decided by how well you did on the state mandated tests, probably administered at about 16 or so. No waste of money to send people who will never graduate to colleges that cost hundreds of thousands of dollars. No preferential treatment to minorities.
Oh, and most of the colleges would be drug free... with police dogs walking the halls.
Who you married would still be a free choice, as long as it was someone of the opposite sex. I don't know if mixed-race marriage would be allowed, but it probably would.
RAP music would probably not be legal.
While the schools would be publicly funded, ones that consistently fail to educate students to the federally mandated standards would be investigated, broken up, etc. School choice would still be allowed, as in you could send your kid to the state school of your choice, or to a private school with a voucher.
Federal drug laws would not exist, and be rigorously enforced. Border states would have armed soldiers patrolling the borders to prevent foreign nationals from infiltrating.
Individual rights would have meaning, as would personal property. More so than today. The population of citizens in prison would probably be smaller than today, as prisons would be harsher and people less likely to be repeat offenders.
Church would be voluntary (probably).
And I think EITHER of these would be better than what we have today.