Years ago when I first visited Asia, budget airline carriers didn't yet exist and the usual situation of a flight from one place to another was going to cost you an arm and a leg. Therefore, myself and all other backpackers didn't even bother to look into the cost of flights from one place to another and would instead opt for trains, buses, and in dire situations minibuses.
These days in most of these countries the flights between locations that are connected by train carry with them a price that is nearly the same regardless of which you choose. Basically, unless you have some particular reason to travel by train such as a ton of baggage (which if that is the case you are doing backpacking wrong in the first place) there is normally no financial benefit to train travel
When I was last in the parts of the world that have affordable train travel - and this normally means much older and very slow trains the likes of which exist in South East Asia, the cost of train tickets had gone up dramatically compared to buses and the cost of flights, due to the rise of popularity and existence of budget airlines had gone waaaay down. In many instances, if not most instances, the prices for travel between two cities that had train stations (and therefore probably have an airport nearby) was almost always cheaper to go by plane.
Also, obviously, a train takes significantly less time.
There are some fantastic advantages to taking the train though and if the price is around the same, you may wish to consider the train anyway.
For one thing, your seat on an airplane is going to be cramped, that is the very nature of a budget airline and even on the "full-service" airlines as well. You need to be a high-falootin fancy-pants rich fella to get a seat this size on a flight and on the budget airlines, they normally don't even have business and first class anyway, not that peons like you and I could afford them anyway.
Also, there is the added benefit of dining cars
Ever felt like your knees were going numb on a flight? Well that is never an issue on a train because you are allowed to walk around and also encouraged to make your way to the dining car. Now I'm not going to lie, the food on offer isn't exactly gourmet and I would stay away from any baked goods and stick to hot foods in order to avoid food poisoning, but at least it is an option. Also, they tend to serve a wide variety of cold drinks and even beer in these things, and for me, that is always a welcome addition.
Also, if you are on a long haul ride which takes place at night, the staff will come by at a certain time in the evening, like around 8pm or so and turn everyone's seats into beds. Try getting that on an airplane!
Now if you are are over 6 feet tall this is going to incorporate hanging your legs out the side, which is frowned upon in Asian cultures, or curling up a bit but it certainly is preferable to a seat in coach on an airplane.
Obviously, the train takes significantly longer than the flight does but if you are backpacking in a manner that I consider to be proper, the time frame is irrelevant and therefore you should try to take in the countryside and enjoy the ride. You may even meet some cool people in the dining car along the way. That has been the case with me on every one of these things that I have done.
I suppose another downside is that in these countries these rail systems, like most rail systems in the world, were originally designed for the transportation of goods, not people, so if an oncoming train carrying goods is in your path, the passenger train is required to pull over and wait for it to pass. This is pretty much a global phenomenon for countries that have not yet developed high-speed rail. Also, it doesn't go to just everywhere in the country and you will be restricted to destinations that actually have rail lines.
So even though it isn't going to save you any money and it definitely going to take longer I feel as though traveling by train in countries like these is a fantastic way to get around and I always investigate it if it is an option when I am traveling. Well, except in the United States. For some reason, even though the USA has the most extensive rail system in the world, it is a terrible way of getting around.