This is an argument that has polarised some of the people here in the past, specifically about Dyneema rope.
There's no question that steel cable is heavier but it does suffer from the elements too if you don't care for it (I spray mine with WD40, hasn't helped my fairlead rollers but the rope is still ok). When steel rope starts to fray though, it's painful - literally! It also has more mass to worry about in the event of a failure. Most people with steel rope (myself included) don't change their rope very often at all. My winch has been on for several years, still works, still the original rope.
Dyneema rope is different because it can fill with dirt and this is the specific issue that has raised so much argument in the past. The issue is whether or not you actually need to clean the rope, and whether or not the grass/dirt/mud/sand/tree fibres etc cause damage to the rope whilst it is in use. Some say that it does, others say that they've not cleaned theirs after use and the rope is fine. UV damage potential is undeniable although if it's mounted deep in a steel bar like most of ours the sun doesn't really get to it unless it's being used - and even if it's used (like mine) to do more than just vehicle recovery (tree stump removal, oh yes!) it's not really out long enough to do lots of damage.
The real difference will come down to whether you need to save the weight, and whether or not you're happy with the cost to replace the rope when needed.
Personally, I've had my winch for years, I will upgrade to a 5.3T one when I next get an opportunity, but it will keep the cable it comes with. I've never had an issue with steel except for the occasional loose strand which is a real bugger when it nicks your hand.
Winch speed: isn't going to be dramatically different. When you need to use the winch - the sh;t's hit the fan and you need to be self-recovered - ANY progress out of the mire is looked upon with joy. If it's pulling you out at 3.5m per minute or 2m per minute you don't really care, both are progress and both mean you didn't have to call your mate with his Toymotor to try and get you out.