The answer to your question is on whichever airline you hold the highest elite status.

If you hold no elite status at all, Southwest is likely your best option. I'm not impressed with Southwest's irrops recovery, but it will be far better than attempting to travel as a non-elite on a major.

If you are a non-elite and your flight on a major is canceled, your best bet is to simply refund the trip. (It's a "trip in vain" - they should refund you entirely, even for WX.) It's unlikely that you'll even get to talk to a human unless you're originating from a small outstation for that airline.

My good experiences:
- United 1K: usually automatically protected me on the next flight via email, even before I knew my flight was delayed. If I wanted something else, the 1K phone line was available to me...usually quite flexible in rebooking.
- AA Gold: pretty good for low-tier support. Even rerouted me onto Star Alliance for basic WX when I was traveling on an award ticket, something they are not obligated to do. I suppose there's the potential that you'll lose phone support during exceptionally severe systemwide WX, but this hasn't happened to me yet.
- US Gold: experience is a bit dated, but their phone agents were willing/able to reroute to other alliance partners with minimal hold times or waiting for confirmation. I don't know if the merger has made this better or worse.

DL...no elite status...last time I had a cancel with them it was on the outbound, I just had our TA cancel the trip. (To be totally fair, I tried to phone them once and got dumped into endless hold, but I didn't drive to the airport and give their counter agents a chance to rebook. It was a trip I didn't mind killing...)

Southwest is okay...the one quirk they have had in the past is a reluctance to rebook you until you've *actually* misconnected. Sitting in DTW, as my connecting flight at MDW is already taxiing...WN's response was "go to MDW and they're rebook you". Phone agent would not do it. Not sure if things would have been better if I'd been on the website or at a counter agent...