No, the Soyuz is by far our safest spacecraft. It’s got multiple safety systems including a launch abort system that was actually used in 1983 and it saved all the crew. The Space Shuttle didn’t have a launch abort system. Though the first few Soyuz were dangerous, they have learnt from them. And the main thing about the Soyuz is that the Russians, having found a good design, have stuck with it for decades and so achieved an excellent safety record.
It’s going to take a while for any new ways to get humans into space to match their record, just because it costs so much to launch into space. If the new space companies have a single crash that kills all the crew, then that will set them way behind the Russians and it would be hard after that to establish their spacecraft as safer than the Soyuz. So it’s like a “gold standard” of space safety.
The Apollo spacecraft had a good safety record too, apart from Apollo 1, but they didn’t have anything like as many launches and of course Apollo 13 came close to disaster. The Space Shuttle obviously didn’t have a good safety record, 135 missions with two crashes List of Space Shuttle missions. The Chinese have an excellent 100% safety record so far but that’s with a total of only six flights to date. Shenzhou program
The Soyuz hasn’t had a fatal accident since Soyuz 11 in 1971. Their launch escape system has only been used once, for mission 45 in 1983, which is also the only time to date that a launch escape vehicle has been used in any mission with crew on board. Everyone survived. They are now on mission 132. That makes it 111 missions in a row so far without a fatality and only minor issues since 1983.
If we do get commercial flights with hundreds of missions into space every year, then maybe one of them will beat the Russian record. But the way SpaceX is going, then they are talking about “fun but dangerous” missions pushing the envelope of what is possible. Their second mission with humans, they say, will send them around the Moon, a very risky flight. If they do follow that approach then I can’t see them matching the Soyuz safety record. But I think that this may be more like inspirational “sales talk” to get everyone excited about their human spaceflight program. I hope so.
Their ideas of using the same rocket for human and for unmanned flight may let them do many more tests with unmanned records, earning money each time, if they don’t keep changing the design. If they do it that way, so that the rocket humans fly in is the same one that the cargo flew on, then they could perhaps rival the Soyuz safety record.
They do also have the issue that they are going to load the fuel after the passengers which former astronauts and other experts have said is a safety issue as when the fuel is loaded there’s a chance of the rocket blowing up with humans on board. If that happens, even if the launch abort system works and sends them to safety, well launch abort is not meant to be triggered at all, is very much a last resort. So I think they have an extra challenge there, to demonstrate that this innovative approach of launching the fuel after the passengers is indeed safe, and then they would need many safe flights to begin to rival the Soyuz record.
See also my Why I Wouldn't Fly With SpaceX To The Moon As Soon As 2018 - If They Paid Me A Billion Dollars
It’s the same with the others, Blue Origin, Virgin Galactica - and indeed the Chinese, it’s just going to take some time for them to rack up over 100 spaceflights to show statistically that they are safer than Soyuz. And it’s hard to prove that just by theory and modeling as that often goes wrong.
I think our best bet of beating the safety record of Soyuz myself, in the near future, is the UK / ESA’s air breathing Skylon. The reason is because it will take off and land horizontally, like a jet plane from a conventional runway (though reinforced to take the extra weight of fuel during lift off). The whole thing is re-used “as is”.
Artist's concept of it taking off into orbit
It’s like SpaceX - it can fly either crew or cargo (not like the Space Shuttle that had to have crew on board), so they can have many cargo flights before the first crewed flight. But with such rapid turnaround, every Skylon plane could fly into space every week.
If they had two or three such planes eventually, each flying into space with human passengers every week, they could beat the Soyuz record in a single year. And because it can take cargo into space without humans, and can earn income for every cargo flight, and basically flies humans just like the cargo, controlled from the ground, then there is no need to fly humans early on. They could have a hundred cargo flights before flying the first humans into space if they wanted to.
There are other ideas for space planes like that. But it’s the only one that is at such an advanced state and with the UK and ESA committed to it, then I think it has a decent chance of reaching fruition.
It may be ready to fly some time in the 2020s. If it is as good as it seems it might be, it could beat the Soyuz safety record within a year or two of whenever it first starts doing regular flights every week into space with passengers.