I'm a little late to the thread, but I'll chime in anyway. I have both, and I shoot both regularly. In fact, I also refurbish QL17's, and I have about 35 on hand right now (give or take). You really couldn't have gone with either camera, but, truth be told, I prefer the Minolta for use, and the Canon for resale.
With your Canon, I feel pretty confident saying you need to replace the light seals. All of them. There are 4 plus the felt one (which usually doesn't need replacing). Three on the door, and one around the double exposure button on the bottom. The 3 on the door are pretty easy, albeit tedious and somewhat messy. The one around the button needs to have the base plate removed. The hardest part is cutting a circle (or reasonable facsimile) for the button to work unobstructed.
The battery that I use is the air-zinc Wein MRB625's 1.35v, which is the correct voltage. You can get them on ebay pretty cheap. They only last a short while, so you may want to stock up on them (they discharge when exposed to air).
Why do I prefer the Minolta? The lens. It's a Zeiss design collaboration, and is amazingly sharp. I also like the size. It's a very subtle camera, and people don't think twice about it. Also, it doesn't have light seals that deteriorate like the Canon. And, it takes LR44 batteries, which are really easy and cheap to get. If you buy one 4LR44 battery, you can open it up, and there are 4 LR44's inside. Sweet.
But, they are both really good cameras, and if you do get the 7sII, let us know which one you like better.
And, on a side note, if you need light seals for the QL17, let me know.