I agree with Gilladian. I a one-player, one-GM campaign can work fine, but I also think that building a full party is usually a mistake in this case, as is having the GM play half of the PCs. Play to the strengths of the set-up, not the weaknesses.
However... to the extent that you and your friend prioritize tactical combat, advancement, and getting of loot, the sorts of urban, intrigue, role-playing and plot style games that Gilladian talks about may not be your cup of tea. If what you want is more in the dungeon-crawl, tactical combat style, then accept that's what you want and build the game around it. I would suggest for this purpose having the player play one character that's a full character (the party leader in terms of story, but not necessarily a "leader" class in 4e terminology), and then have the rest of the party be fairly simple. In 4e, that might mean using some of the simpler Essentials classes, or using the supporting character rules from DMG2, or building some non-PC class characters with basic attacks and maybe encounter powers that fill the role of additional people in the party, without the complexity. And then have at it. You'll have more of the feeling of a two-player tactical wargame, but that can be fun, too. It's not my preference, and I would rather use a one-player game to focus on a single character, but your preference may be different.