Many low-cost airlines have bad reviews for food or in-flight entertainment. But these are not my concerns. I prefer not to eat on the flight and save one thought dollarS instead. However, something that I care about is the safety of the flight. If these airlines try to minimise the costs do they do the same on flight safety? Is Jetstar as safe as Qantas or are AirAsia/LionAir flights as safe as Qatar Airways?
Related but narrower scope: How safe is it to fly with Ryanair?
Low-cost carriers (LCC) cut many corners, but they generally do not skimp on safety: having a single accident can easily bankrupt an airline.
That said, it's a big world out there and not all LCCs are the same. I'd roughly bucket them into 4 groups, 3 of which are generally OK:
Those owned by mainline/legacy carriers generally apply the same safety standards as their parents: this includes eg Jetstar (a Qantas subsidiary) and Scoot (a Singapore Airlines subsidiary).
Major LCCs also tend to place an emphasis on safety: Ryanair is one of the world's largest airlines but has never had a fatal accident, while AirAsia used to contract out its maintenance to Lufthansa Technik and has a solid (albeit imperfect) record.
LCCs headquartered in developed countries are subject to the same strict regulations as all other airlines in those countries, and this is why the safety records of LCCs based in eg the US, the EU and Japan are quite good.
The one group to be wary of is independent LCCs in developing countries, which can lack both a safety culture and strong regulation. Indonesia is a bit of an unfortunate poster child here, with LCCs like Adam Air, Mandala, Sriwiyaja etc crashing on an alarmingly regular basis.
To answer the original question: Batik Air is actually not an LCC, but the full-service wing of Lion Air. (Wings Air is Lion's even-LCC-er wing.). Lion is a major LCC that's been around for a while and is authorized to fly into countries like Singapore with strict aviation oversight, but their record is distinctly not great, with 6 major (hull-loss) accidents since 2002. Personally, they would not be my first choice and for domestic Indo flights I'd go for Garuda or AirAsia even if it cost a bit more, but if there are no other reasonable options I'd still be OK with them, since traveling by bus or ferry in Indonesia is even more dangerous. YMMV.
Generally (I.e. not only for LCCs, but for traditional airlines as well) the country of registration is much more relevant than the business model: in some countries oversight is lax if not inexistent, corruption may be rife. The economic situation may also mean parts are hard to come buy, so aircraft will fly with more non-functional systems than normally allowed, or systems fixed with various quantities of duct tape. Planes are also usually older, sometimes a lot older.
One can check the EU airline black list for reference. Those airlines are banned from flying in the EU (totally or partially), which is the sign of big problems in their maintenance or oversight processes. You’ll notice that some countries are represented a lot on that list.
In countries with a strong oversight, LCCs are subject to the same procedures and controls as traditional ones. Cutting corners in services offered is one thing. Cutting corners on safety, with the risk of having their operating certificate suspended or revoked, is an altogether different story.
There is a already a very good answer but here is some auxiliary data.
All of this leads to the same conclusion: air travel is very safe and there is no discernable difference between LCCs and main line carriers in most parts of the world. Most accidents happens with smaller carriers in more remote areas involving turbo props.
Indonesia is indeed a bit of on outlier there with two major incidents in the last 5 years. This being said: Indonesia has over 100,000,000 passengers per year so the individual risk is still extremely small: I flew AirAsia from Denpasar to Djakarta earlier this year and I lived to tell the tale :-)
Safety is never an issue, no matter how much you're paying. The pilots are still licensed, the airlines still go from point A to point B a large number of times per day, the planes undergo the same checks, etc. If discount airline meant high risk of crash, you wouldn't have discount airlines.
I've been flying nearly 40 years (crazy to say), and have mostly flown discount airlines. I've never had any issues, aside from lack of comfort or rude staff in certain cases. That said, Ryan Air, as you specifically mentioned them, is one of the only airlines in the world I refuse to fly again based on just how bad the service was. Safety won't be your concern, but if you don't like flight attendants being hostile to you for no reason, you might check out a different airline.
First of all, all airlines are considered safe as long as they follow best practices.
The ones that do not follow them tend to get blacklisted. You can look up whether the airline you are flying with is blacklisted.
Secondly LCC carriers focus on short turnaround, to mitigate reimbursements paid to customers. In order to achieve that they develop practices that are actually beneficial to safety:
