All bits are capable of causing discomfort/pain. I don't think any bit can be called 'soft', but some are milder than others. All bits will be uncomfortable to the horse until they're desensitised to wearing one - just like first learning to wear a tie or glasses is to us. Some horses can find any bit a problem, despite being well desensitised & educated.
Some bits, such as thin or twisted wire ones, or ones that are unsuitable to that horse or the wrong size may be uncomfortable to the horse even with little or no pressure on the reins. Some bits, such as leverage bits(the longer the shank, the stronger the leverage power), mechanical 'hackamores', ones with curb chains, certain styles of mouth 'ports'(the hump in the middle of some unjointed bits), single jointed bars with shanks, such as 'Tom Thumbs' can create strong pain with very little pressure from the rider. Even jaw/nose breaking pressure if used strongly, roughly or in case of accident(bit gets caught, etc) curb chains & leverage are combined, such as Pelhams, mechanical hacks, etc. Some bits can give unclear signals to the horse, such as mechancal hacks who's shanks operate independantly, bits with shanks and joints, etc.
The bits I consider the safest/mildest are double jointed snaffles, unjointed, port mouthed(so long as the port is comfortable for that horse, not big or angular) bits, with or without *short* shanks, depending on riding style.
To a degree it depends a bit on what you're doing & what the horse likes & how his mouth is built - a fat bar in the mouth of an arab or pony might be very uncomfortable. Eg. Using a western shanked bit for western style, loose rein & neckreining is one thing, but using it to ride english and use short direct reining will cause problems.
It also depends largely on the horse's education and the rider's skill. If you're going to 'ride short' and end up putting a fair amount of pressure on the reins either becuase of your insecurity & lack of skill, or because of the horse's lack of education, any bit can be terrible. A single jointed snaffle for eg. Will have a 'nutcracker' effect on the horse's tongue and the joint can gouge the roof of the mouth.
I believe that horses are best started without a bit, for a number of reasons(look up Dr Cook's site for more info) in a halter, (non mechanical)hackamore or bitless bridle. The horse needs to learn to yield to pressure in all ways(not just rein pressure), get used to being ridden & following instruction and comfortable & happy about it.
Then, once the horse can be ridden in such a way that the bit will only be used for communication rather than control, a 'mild' one can be chosen if the rider wants - say for showing or clubs where it's required. The horse will first need to get used to wearing it without pressure, before it's taught to be directed by it. Only very skilled & educated rider/horse pairs should then go on to a 'stronger' bit if they desire it for competition or the likes.
Problems that often lead to people thinking they 'need' a 'stronger' bit are to do with horse &/or rider education & skill - or lack of - or from pain or fear of pain. While (most?) pain while riding can be attributed to saddle issues, often it is the bit or it's use that is the cause and I've found time & again, both in 'retraining' horses myself and helping riders that simply removing the bit removes the issue, many times with little or no additional 'training'.