Upgraded Falcon Heavy as an alternative to SLS

At the moment, there's a lot of discussion involving SLS, particularly about how unaffordable it is, and the difficulty of low flight rates (reliability, etc).

The counter argument is we need it due to its large payload capability and high-ISP upper stage. The latter is particularly important for anything beyond LEO. An example is the difference in launch capacity to LEO vs. GTO for Falcon 9 and Atlas V; Atlas has a much larger GTO capacity, as a percentage of its LEO capacity, than the F9, due to the high ISP of its LOX/H2 Centaur upper stage. Ker/LOX works well for a launcher, but for in-space use, its lower ISP is a serious drawback.

A better example would be Falcon Heavy vs. Delta IV heavy. Using Falcon Heavy figures from before the Falcon 9 V 1.2 version currently in use (which has oxidizer subcooling, higher thrust engines, etc) because updated figures aren't available, we see 53 tons to LEO, vs 21 tons to GTO (Geosynchronous transfer orbit) so the fraction of Leo capacity to GTO is 39%. For Delta IV Heavy, we see  28 tons to LEO, 14 tons to GTO (50%).

These differences are magnified for interplanetary launches.

Therefor, the argument goes, you need the SLS and its expedition upper stage (essentially an enlarged Centaur) for Mars missions.

However, there's a theoretical alternative; SpaceX's in-development Raptor engine, which uses methane/LOX. That combination does not have the ISP of hydrogen/LOX, but methane is denser, so you save mass in tankage to the point of nearly breaking even. The Raptor would enable a Raptor-based MethLox upper stage for Falcon Heavy.
With such a stage (stretched from the current to allow for increased propellant mass) you'd have a very different beast - a high ISP upper stage with significantly more propellant.

By essentially shifting mass to the upper stage, you do away with much of the motive to crossfeed. You also end up staging at lower altitude and velocity, making recovery is the 3 1st stages easier. And in so doing, you shed a lot of mass earlier - mass you no longer have to use prop to accelerate.

The big impact is on payload; people who can crunch the numbers better than I can get around 129 tons to LEO for this configuration, and it'd have a better LEO to GTO fraction (and thus a better LEO to Mars fraction) than Falcon 9. Not quite as high a fraction as the envisioned version of SLS, but very close.

A further upgrade would entail dissolving hydrogen in the methane (this gives an ISP boost, and methane, like propane, is easy to dissolve hydrogen in).  

What you would have at the end of all this is a Falcon Heavy with a Raptor upper stage, with a payload capacity very close to that of SLS's claimed capacity; 130 tons for SLS block II, vs. 123 tons (expendable mode) for Falcon Heavy/Raptor Upper stage with straight methane (dissolving some hydrogen in the methane would boost ISP and thus payload, but I can't find figures on how much).

Falcon Heavy could have its Raptor upper stage within a few years if it's in development now. Compare that to SLS, which won't have the first flight of SLS block I (56 tons to LEO) until about 2020, with Block II waiting at least until (per the budget) 2033.

This Falcon Heavy with a Raptor upper stage may also not be as theoretical as I assume; it negates the need for crossfeed, and I note that SpaceX cancelled its plans to develop crossfeed for Falcon Heavy. Also, the US Air Force is partially funding Raptor development, and the contracts stipulate that Raptor is for Falcon 9 and Falcon Heavy upper stages.