Hard fork the longer chain wins but the older clients could choose to keep their chain if they want to. The fork with the most users is the fork that has value, that's democracy.
Not at all. Hard fork means that the chain is now two independent chains. On each of these two independent chains, there is consensus. There's no interaction any more between the two chains, they are now two different crypto currencies. The market cap of the original chain will now be split over both prongs. Of course, users and miners might all flock to one of the chains, and abandon the other one. Or not. In the end, the users will decide upon the market cap split, and the miners will follow.
Soft fork, blocks are created that are not rejected by older clients but are meaningless to them, forcing them to upgrade. That's not democratic. There is no option to keep their own chain, there is no choice. That's not democracy.
That is exactly democracy: the majority imposes its will on the minority. What you call "democracy" is what is called "consensus".
As long as the soft fork doesn't have a majority OF MINERS behind it, it doesn't impose its will on the others. Once it does, there's NO FURTHER OPTION.
What is important to realize, with a soft fork, that is are not the *users* but the *miners* who impose their majority on everyone. With a hard fork, even if only 10% of the miners continues on the old chain, maybe 90% of the users prefer the old chain, and the old chain coin will get 90% of the market cap. This is extremely lucrative for the 10% of miners, and the miners that chose the new pron (90% of them initially) will revert to the old chain because it is more lucrative. In the end, the mining distribution will follow the market cap, determined by the users (they determine, on exchanges, how they value the new coin versus the old coin, of which they hold, initially, equal amounts after the hard fork).
This is not the case of a soft fork. When a majority (51%) of miners, and miners only, whatever users think, applies the soft fork, it is imposed on everyone: the minority of miners have to follow, there is only one chain, and the users have only one token and cannot "vote with their money" as there is no other token to buy.