At a conference aimed at answering this question, carried on C-SPAN, a number of distinguished experts described the many ways the general election, stretching from about June to November every four years, would be different from the current system. Here's a summary, mixing different comments and my own views without attribution and with a little license:
1. Brand. The major parties would create national brands for their candidates. They'd advertise on big national television events, like the Olympics, fall baseball, popular tv shows, and the NFL Sundays. Networks for the first time would get a lot of advertising money. The brands would aim at broad popularity. Extremist views, whether for open borders or open season on immigrants, would be discouraged.
2. CPM/vote. With every vote worth the same, the major parties would assess the cost of reaching every possible vote regardless of geography. To do so, they'd consider social media ads, local newspaper, local broadcast, local radio, and even billboards and mailings. Like all modern advertising of products, they would aim at assessing the cost of reaching and the ways to appeal to voters on the most individual level possible. For a change, all voters would get attention, and views that appealed to the biggest blocks of voters would be the views espoused by the parties. The parties would change more than the views of the voters would change. As a result, broadly popular views would be endorsed by both parties, such as action against climate change, for gun control, against greater income and wealth inequality, and for cheaper health care. The parties would debate tactics more than premises on these topics.
3. The result of a cost and issue based analysis would be to find a way to present a pitch to everyone, everywhere. Neither party would take for granted an outcome in any precinct. There'd be no reason to do so. The closer the election, the harder the parties would work to get the attention of the undecided and the possible non-voters, while also building get out the vote systems everywhere in the country. There are several hundred thousand possible Democratic votes in North Dakota no Democratic nominee tries to reach and there are also several hundred thousand Republican votes that in the general election their candidate does not bother soliciting. North Dakota would get attention at last. This is just an example.
4. Turn-out would rise, especially among Latinos and young people, two populations typically ignored and hard to reach in the general election.
5. The winning candidate could truly claim legitimacy.
6. More money would be spent, but as it would shift more toward social advertising and the number of voters would rise then the cost per voter would go down.
7. The parties would use the primary process to increase registration. They would maintain registration records through to the general and use that data to reach voters. Generally participation would rise to registration levels, and therefore voting participation would increase by as much as 20% to 40% in most states.
8. With every vote mattering equally, the parties would argue for better ways to enable voting, such as voting by mail and more access to the polls. The parties would still be motivated to suppress voting for the adversary, but they would limit those efforts to disqualification as opposed to altering methods of voting, because in every precinct both major parties would have votes to get, as opposed to the current system where one party has little to no motivation to battle for votes in as many as 40 states.
9. The intensity of pursuit of voters in swing states would decline, and the result would be to provide greater continuing support of both political parties by the national party in those and all states. The parties' state structures would rise in importance.
10. Third parties would have a much reduced chance of affecting the outcome, whereas with the current system the much disregarded Nader cost Gore the plurality in Florida in 2000 even though Nader got almost no votes. Indeed, only a national party, built on a broad coalition, could hope to win a national general election if every vote mattered equally.