In my opinion, as someone who owns an IGH bike (Alfine - 8 speeds), it has some drawbacks compared to a derailler. It feels a little more sluggish, not quite as efficient, and gears are spaced farther apart than they are with a derailler. For below freezing weather, it's nice that it doesn't have any gears on the outside that could get frozen up, but more just riding in rain an igh with a chain doesn't have a lot of benefits, imo - rain doesn't cause shifting issues, and the issues it does cause - like a squeaky chain - still happen because you still have a chain.

So if you're just riding in rain, my advice would be to stick with the regular derailleur which is cheaper and slightly faster.

If you really want something more weather-proof, like I said before I think IGH+Belt Drive is the way to go - with no chain, there's a lot less hassle. To be fair I don't own one though, so if there's issues I probably just don't know about them.

The one alternative I've heard of is doing an IGH plus a full chain case which completely encloses the chain and keeps dirt, water, etc off of it. I don't know if it's possible to add one aftermarket, though.

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Regarding stopping, I've had some pretty terrible experiences with my Dura-Ace 7800 pads - seems like with rain the stopping distance is about doubled. I've heard good things about the Koolstops, as well as Swiss Stops, and much better things about the Dura-Ace 7900 pads as well. I bought some koolstops for one of my bikes - but I haven't tried them yet.

With disc brakes, I can't even tell the stopping difference in the wet vs the dry. In the winter, there's less worry about frozen rims stopping them, and they don't grind salt and sand from the road into the rim (I suppose this is true when it rains, to a lesser extent, as well). They're nice that way. But they have drawbacks as well -

For starters, the bike needs to have the mounts in the frame for disc brakes. Does that bike have them built in?

For another, some disc brakes can still be finicky. I've had 2 bikes with disc brakes, and my dad has one. He's always had problems with his BB5's rubbing and making nasty noises when braking. He replaced the back one with a BB7 and it's better, though not perfect.

I have a Specialized mountain bike with Avid Juicy 7's. They've been absolutely flawless - great stopping power, no squeaks - nothin'. To be fair, being my mountain bike I don't ride it in the rain.

My winter bike also has Alfine disc brakes on it. It was a giant pita for a while - discs kept rubbing. Eventually I got the front fork replaced, the mechanic thought maybe the hole wasn't drilled in quite the right place on the old fork, and it's been a lot better. It didn't rub last winter which was way better, though it did still sometimes make some squealing noise when stopping (sometimes it does, sometimes it doesn't).

So disc brakes can be great, but they can also be really annoying.