Paul vs. Jeb
Paul vs. Walker
Paul vs. Christie
Looking at the contrasts...
Jeb VS Paul:Security state VS Civil Liberties
Compassionate Conservative VS Small Government
Establishment VS Outsider
Elder Statesman VS Newcomer (Paul's political career began after Bush's tenure as Governor ended.
Christie VS. Paul:Accomplishment VS Vision
Bipartisanship VS Ideological Purity
Bush Appointee VS Ron Paul's son
Ruthlessness VS Morals
Walker VS Paul:Accomplishment VS Vision
Political Expertise VS Outsider (Scott Walker has been in elected office since he was 26.)
A career exclusively in Wisconsin VS A career in DC
Firm opposition to Democrats VS Outreach
Almost definitely Paul vs Bush (assuming he runs). They're the only two Republicans really capable of putting together a national campaign structure.
If Bush doesn't run, I expect it to turn into a 3 way race between the establishment figure, an evangelical candidate like Huckabee that catches fire, and Paul.
The real trick behind beating Paul is to find an establishment figure that the evangelical right likes. I guess that's why they want Bush even with his current baggage; the Bushes still have major credibility with them from W's presidency.
If Jeb Bush and Rand Paul run, there may be an opening for someone who is in the party's mainstream but lacks the baggage of Jeb Bush's name. They might also make an anti-dynasty argument since Rand Paul's dad also ran for President. I doubt there would be a three way race for long, since the tendency in Republican presidential primaries when one of the top candidates is for another to take that place (Giuliani's fall helped McCain in 2008, the succession of anti-Romneys in 2012.)