Inca RailInca Rail
Inca Rail has been running trains to Machu Picchu since 2013, and has provided much-needed competition on the route. Their entry-level class (known as Executive) compares well to PeruRail's Expedition class, and they also have First Class carriages which are similar to the Vistadome. Inca Rail don't have separate First Class trains in the way that PeruRail operates the Vistadome, however - more like British trains, they just have separate carriages on the same service.
Inca Rail Executive Class
Inca Rail's Executive class is pretty similar to the Expedition class on Peru Rail. Again, you have reasonably comfortable seats, all with a table, and you get a free drink and snack. The windows are the same size as the Expedition, but you don't get the roof panels. Because the two trains are basically similar prices, we would probably go for the Expedition but would have no hesitation in using the Inca Rail Executive class either.
There are several services a day between Ollantaytambo and Machu Picchu, but only one which runs right the way through from Cusco. This departs at 05:55 and gets you into Machu Picchu at 08:48 - all the Inca Rail services have a slightly shorter journey time than the Peru Rail alternatives.
Inca Rail First Class
While the Executive and the Expedition are pretty similar, Inca Rail's First Class option offers something a little different to the Vistadome, in that you actually get a full at-seat lunch service as well as little bonuses like a welcome cocktail. It's just a little more expensive than the Vistadome (by around £10 or so) but if you'd like to arrive at Machu Picchu having had lunch and ready to explore, than it's well worth considering.
The only slight downside is that the First Class carriages only operate on the 11:15 departure between Ollantaytambo and Machu Picchu - no problem if you stayed overnight in the Sacred Valley beforehand, but if you're coming from (or going back to) Cusco then we'll need to arrange the extra transportation for you