I started making wine first. I started beer afterward, because wine takes soooooo long! I've only been doing this for 9 months, so I'm no expert but I see the differences as this:
Wine is easier and more forgiving
You don't "brew" (cook) wine
In wine, chemicals are used usually- campden, pectic enzyme (for fruit wines), stabilizer, etc. Very quick and easy to use, but a little different than beer.
Wine takes longer to ferment out completely
Wine can be sweetened after it's done, if you want a sweet wine.
Primary fermentation in wine is usually covered with a cloth to keep out critters, but to let co2 escape- no airlock until secondary fermentation.
Also, more fermentation takes place in secondary than with beer- for beer, the secondary is more of a clearing tank. In wine, fermentation does happen in secondary.
Wine is more forgiving because it has a higher alcohol content so it's less likely to get infected. Not impossible, but less likely. Vinegar can happen if it gets contaminated.
The equipment is basically the same (you need a corker instead of a capper) and so is the process. If you find a recipe you like and follow it closely, you should be just fine. I'd recommend doing some reading on winemaking- jackkeller.net is a great site. It's hard to navigate at first, but go to "basics" and he'll tell you everything you could ever need to know and it's easy to understand.
Lorena