This is a point that I hesitate to mention because there are so many variables in this statement. However, generally a bandsaw is safer to use than a table saw.
This is not an excuse to be lazy. Caution should be used when using either of these machines and you should be 100% confident before carrying out any task. I will also say that this statement comes purely from my own observations of working in a Tools and Machinery store for 5 years, woodworking since 2012, and training students on using these machines.
With a bandsaw, the blade is travelling down towards the table which means the cutting force is pressing down. A table saw however, is cutting towards the operator. One of the most common accident on machines is kickback where the material is thrown from the machine into the operator. This is where cutting forces come into play.
When cutting solid wood, springback occasionally happens. This is where tension within the wood releases once it has been cut and causes it to spring apart or pinch together. Either of these can be problematic, but the main danger is when the material pinches.
If this happens on a bandsaw it usually isn't a problem. The wood is cut and by the time it begins pinching the material is clear of the back of the blade. Even if it was to pinch the blade, the cutting force is towards the table meaning the chance of kickback is negligable. Don't get me wrong, kickback is not the only danger here. But its the one we are focusing on in this example.
On a table saw however. The wood has potential to pinch on the back of the blade due to the fact the blade is larger and the material is in contact with more of it at once (Which is why table saws are so good for straight cuts) On a spinning table saw blade, the cutting force on the front of the blade is pushing diagonally down towards the operators mid-section. On the back of the circular blade, the direction of travel is diagonally up towards the operators face. If the material was to pinch at the back of the blade, its going to be lifted off the table and thrown back towards the operator at speed.
This is the importance of using a riving knife or a splitter on a table saw as it greatly reduces the risk of this happening!
The other thing a riving knife prevents is the material twisting away from the fence and riding up the back of the blade. Again, throwing it towards the operator.
The Safety Police
Now I don't want to come across as the safety police when stating these points and I know there will be lots of people who give me flack saying “Ive used a table saw 30 years and never had a problem”
That's great, but giving that advice to an inexperienced person who has no idea of the potential dangers when using a machinery is just selfish and irresponsible. I've seen the results of this and the ignorance sickens me. Don't get me wrong, I think it's great that companies such as SawStop exist, the innovation is incredible. But the fact they HAVE to exist is a real shame. If you want to see what kickback is, have a look at this video. The main danger you will face when using a bandsaw is material rolling. Specifically when cutting round objects either by ripping along the length or by crosscutting. The best way to support round material is by creating vee shaped cradle for it to rest in. Also when cutting round objects, you need to watch out for blind spots. This video is the best demonstration of that (Its 30 seconds long and is not graphic.)
It's worth saying however, both of these dangers on the bandsaw are also present on a table saw.