I use the Avent storage containers and I used to have problems with leaking. Two tips and you won't have that problem.
1) DO NOT OVERFILL THE CONTAINER. The tick marks go up to 7 ounces, but don't put any more than 6 in there (which is what they are advertised to hold). Any more than that and the milk gets into the seal.
2) Don't squeeze the container as you screw on the lid. The best way to attach the lid is to put the container on your counter and then screw the lid. Don't hold the container or squeeze it at all - if you do, it misaligns the top.
My only complaint is that they are expensive and I'm storing a lot, so I need them in bulk.

I have loved having these containers to freeze breastmillk in. They are easy to use. I pump a little bit at each feeding and fill up containers all day in the fridge and then at night-time, I transfer the containers from the fridge to the freezer. Also, I haven't found any leaking or problems putting the lids on properly. Just be patient and learn how to do it right the first time, and no more problems to speak of arise. My one complaint is that you can get extra containers (they are all pre-sterilized) but you can't buy just extra LIDS which I would really love. So thats my one complaint. Otherwise, I am loving these containers!

I decided to try these for freezer storage since the bags seemed like they would just be a big mess to deal with. I really like these containers and have not had any problems with them. I agree that you have to get it "just right" when screwing on the lids, which can be frustrating. But once the lid is in place and tightly secure, they store the milk perfectly. I haven't noticed any change in my frozen breast milk, ie the bad "taste" and/or "smell" that others have experienced.

If you have used breast milk storage bags in the past, you will immediately fall in love with the Via containers. They are sturdy and withstand freezing and thawing. With bags, there is the problem of how to store them in the freezer to protect from abrasions,rips, cracks or holes which render your precious milk useless. Pumping takes time and energy. The Via system is not perfect, but you can pump directly into the storage containers, they stack well, and they provide a durable plastic shield. It is true that the the screw on lid design has its flaws, although I haven't had any leaking problems. I say start with a smaller package and then make you storage decision.

I was a little skeptical when I first bought these Advent storage containers. That lasted a day. I found that not only did it freeze milk and other items, store liquids and solids, and had a handy adapter to become a bottle, but it didnt leak! My husband even found that he really liked the storage containers. Especially when it came to putting it with a nipple/adapter. If it makes his life easier, it makes mine. Now that my child is older it makes great storage containers for snack items that I toss and go. We also use them for the baby food we make, whether we freeze it or just put it in the fridge. We have worn out our old containers after a year of heavy use and are looking forward to purchasing more as our new child arrives soon.