If bitcoin price have increased, I can decide to convert some to USD or stable coin. Which one is better? Or is there other alternative which can be comparable with bitcoin in a way it would be independent and having full control characteristic.
There's no stablecoin that is safe, just that they have different degree of risk when you compare all of them. We have had several of them and more are still coming to the market but first we have to look at each of them:
Centralized stablecoin: This one's are pegged to a dollar bill and other assets like treasury bills that can be converted with stressing the liquidity behind them but often times, the companies behind these stablecoins (USDT, USDC, BUSD and many more) are not free from regulatory scrutiny, BUSD for example has fallen and it's still fallen down because Binance which is the face of the company is duelisting the pairs and have instructed customers to convert them to other stablecoins on the exchange.
Decentralized stablecoin: This is a decentralized stable currency that is pegged to the amount of a dollar and the advantage of this is that is open source which means people get to see what is happening and how it's regulated and users can even deposit a asset to take DAI. There are many of these stable coins that are been launched but protocol manipulation made them fold up before time.
My suggestion is this: If you are going for centralized ones, pick USDT and if you need a decentralized stablecoin to trust and have high peace of mind to others, go for DAI instead.