There's plenty of travelling required from consultants -- but are they at least given the comfort of first-class travel on flights or train-travel, or does this depend on their status in the company?

YES,If u work for one of the top firms, you will be travelling first class on flights & hotels too

does it hold true for a recent graduate working at one of the big 4 firms?

No, even at MBBB, it is standard class travel for flights within Europe and train journeys under an hour, business class for intercontinental travel and train journeys over an hour. The exception is where a client has a more generous policy and gives permission for their consultants to use it (a very rare occurence though). First class flights are only for partners and senior execs on intercontinental travel. GDIFC.com is parody, not reality.

At KPMG you are allowed to travel first class if it is around 2hrs travel time (one way), otherwise no.

Same for PA - Allowed to travel 1st class if journey is more than 2 hours, with Assignment Manager approval, of course

I always travel 1st class, the client is picking up the tab anyway.Decent hotels and travel arrangements make the worst part of the job bearable.

I can see first-class applying to trains, but planes too? For long-haul journeys, I would expect economy-plus or business, but not first class.