I travelled 12 sectors on RegioJet between Budapest and Vienna last summer, 8 in spring this year, and have another 6 booked in the summer. Two of the four daily trains between Prague and Vienna go on to Budapest.

As you say, the price differential between RegioJet and MAV/OeBB can be substantial; consequently the trains can be packed full.

The differences between the travel classes are not straightforward and in this instance the information on Man in Seat 61 is not always correct.

Booking on the RegioJet website
The booking process is straightforward, and you can select your seat(s) from a seat-map, although do not expect the direction of travel shown on the seat-map to always be accurate. Bookings are non-refundable in the sense you won’t get your money back if you cancel, but you will get a full credit for future use. This applies to all bookings in all classes. To get the credit, you can cancel online up to 15 minutes before the scheduled departure of your train; the credit can be used immediately for another booking should you so wish. I’ve found this very useful on more than one occasion.

Train composition
Trains are usually composed of five coaches as follows:
1 – Low-cost (open-plan)
2 – Standard (Astra open-plan)
3 – Standard (compartment)
4 – Relax (open-plan) and Business (compartment)
5 – Relax (open-plan) and Business (compartment)

On busy trains, they may add a sixth coach (low-cost), which is usually a compartment coach.

Low-cost
These are generally old (1990s) open-plan 1st class coaches (ex-EuroCity and InterCity trains). Seating is 1-2 across (so, great if you are a solo traveller) and each row has its own window, airline style. Perfectly adequate, if old, and plenty of legroom. No power points, and iffy wi-fi. This is actually my preferred class when travelling between Budapest and Vienna.

Contrary to Seat 61 info, you do get a small bottle of water (same as in all classes) and you can order from the on-board menu (by app only – see below).

Standard
Two types of coaches – open-plan “Astra” coach (seating 2-2 across) and compartment coach (seating 3 across). More modern, and you can order from the on-board menu, and free coffee available.

Relax
Ex-EuroCity 1st class coaches with leather seats, more modern than the Low-cost coaches, but with noticeably worse legroom. Steward service for on-board catering, free coffee.

Business
Compartments of 4 seats (2 facing 2) with a table in the space between the window and aisle seats. Above the table is a mirror - this means that in whichever seat you are, all other people in your compartment are in your eyeline – the two opposite you, of course, and the person adjacent to you in the mirror! Some people might find this disconcerting, but I guess it's perfect for four people travelling together. Plenty of space, however. Apart from the water and free coffee, you also get a free welcome drink – a small bottle of Prosecco or an orange juice.

Catering
The catering is unusual, to say the least.

There are two menus, an expensive menu, and a cheap menu, available as follows:
Low-cost: expensive menu via app only
Standard (Astra coach): cheap menu via app only
Standard (Compartment coach): cheap menu via steward (cannot use app)
Relax: cheap menu via steward (cannot use app)
Business: cheap menu via steward (cannot use app)

The expensive menu isn’t really expensive, just everything is more expensive (I believe EUR 0.60) than the cheap menu, but the cheap menu is very cheap! Example price: Ham & cheese croissant EUR 1; Czech beer (0.5l) EUR 0.80.

The steward service has a disadvantage in that they only take orders at certain points in the journey: between Budapest and Vienna (both directions) this is (1) after departure; and (2) after leaving Győr (about half-way).

Buying by app means you can order throughout the journey, although expect to wait 15-20 minutes for delivery. It also has the advantage that you can use any credit you have from a cancelled trip to pay for your order; you cannot do this if you order from a steward.

Reliability
This is potentially a problem; I have never had a cancelled train but have had several delays, although none were drastic (longest about 30-40 minutes). Also, at Budapest, the train departs from/arrives at Deli station, not Keleti (but they are both on the red metro line).

Overall, I would recommend them. For the longer journey (Prague – Vienna or Budapest), I would go for Business, but personally I would find Low-cost adequate for Vienna-Budapest.