I think at 1 when they get cow's milk, you end bottles. We only give "milk" in sippy cups.
I like the soft silicon tops better than the hard plastic topped ones. It seems more like the soft "nipples" they are used to, without being nipple shaped. There is no extra "piece" used in these cups - like the Playtex sippies with the hard plastic tops. And my older kids used to tell me that "the piece" makes it hard to get the milk/juice - I think that's the point tho...that it requires suction to draw the liquid out. Maybe your son is getting frustrated with the amount of work required to get liquid out of those cups with the piece in them?
We have the Munchkin brand soft silicon topped cups that we started our infant on to have some water or watered down juice. Even when they are not broken, they do leak a bit when turned upside down or sideways.
That said, I don't think ALL sippy cups are designed to not leak. I think they are designed more for the child's comfort and to prevent a whole "open cup" from spilling.
We recently got different sippy cups from Wal Mart that have Lightening McQueen and Mickey Mouse on them. The top has a different style of harder silicon top that doesn't seem to leak. And our 10 mo old is using both the Munchkin brand and these just fine.
If all else fails, try straw cups. He's definitely old enough for them. But then again, those will leak if left on their side or turned upside down. Some kids just seem to refuse sippy cups and will take to a straw with no problem!
Try some new cups over the weekend. Put all the bottles away - out of sight. He'll get used to some new cups quickly if you aren't going back and forth with the bottles.
I hope this helps you!