It's great that you are trying to introduce a sippy to your 6 month old but it is a little early to expect him to be able to master drinking from any kind of cup. It is completely normal for liquid to be running out of his mouth...it doesn't neccessarily mean he doesn't like what you're offering.
It is entirely too early for you to be taking away his bottle or trying to replace formula with juice or water since his main soure of nourishment at this stage of development comes from formula.
My advice is to provide him with formula in his bottle only and water or juice in his sippy cup only. It may take him a very long time to actually drink from the sippy but keep trying because eventually he will drink water and juice from it. You may also have to try several different kinds of sippy cups before you find one that he likes.
What works for alot of people is to provide juice and water in one type of sippy and then when it is time to wean from the bottle (at about a year) put milk in a different kind of sippy.
your goal at this time should be to introduce him to a sippy cup and get him used to drinking from it.. not to get him to drink from it exclusively and it isn't important for hi to have alot of water or juice either.
You're on the right track!! babies do things at their own pace and the only thing you can do is keep trying and follow their cues...it'll happen when he wants it to..not necessarily when you do.
Nuby makes a sport bottle that is similar to a bottle...they also have a sippy with a soft silicone straw..you could try those since they are bottle like. They sell them at Walmart.
Good Luck!!!