For commuting, I have an Ortlieb office pannier, but for the tour 2012 along the Danube for one week, we needed more space for tent, clothes and other stuff (nobody needed in the end!).
I had a set of two small panniers, really waterproof. Then, I had a monotrailer with a "waterproof" bag. So, we bought a set of cheap panniers at ALDI (9,99 €) for my front rack. Then, we bought a set of panniers at LIDL for Monika's rear rack. It's price wasn't much higher than the one of the ALDI panniers. Both kind of panniers came with a rain cover!
In short, a pannier, which needs a separate rain cover isn't waterproof. A pannier, which is leak by structure will not become waterproof with a rain cover. The only benefit with this bags is, that the water, which comes in at the top, can leave the pannier at the bottom without problems.
But all that, we knew before. Monika had informed herself about the agrarian forecast. It says no rain the next 8 days. We felt nearly"rainsafe"!
...but it wasn't so, we had rain on 4 of 9 days. Heavy rains up to continuous rain! If you travel with a tent, you have nearly no chance to get your stuff dry. So, we had a lot of stuff (and weight) in our panniers, but the lion's share was wet, we were not able to use it. At the very most diving equipment could be transported suitable in this "runoff ditch".
Anyway, I had no need afterwards, to explain my wife the price of a good pannier.
Such panniers (ALDI) are of no earthly use. The maximum use is, for transporting rain gear, because the panniers will get wet inside at that moment, they will be empty. On our tour, it was senseless to transport clothes in that panniers...
It's to bad about the resources, which were wasted for such a useless product.
The counterpart from LIDL. A fit like a sack of potatos in a cellar nook! Here also a rain jhonny, which only can do one job good: keeping the taillight from being seen!
No, I'm not peeved at the panniers. Afterwards, I laughing about them, but it reminds me, that it is no fun, cycling around with no dry clothes in the panniers. I do not rail against LIDL and ALDI, because their panniers can exact, what you have paid for: You can fill them with stuff form the top and they will keep your stuff for one week without falling apart. That's proofed! But for cycling to China, they would be a little bit suboptimal.
Meanwhile, we use Ortlieb and Vaude panniers. They make no problems, are waterproof and... not really cheap! But they will become cheaper the longer we have them.