Depends on park I am headed to and the expected weather.
If I'm headed to EPCOT and it's going to be raining lightly/moderately on and off all day - I might take an umbrella. The walkways are wider here - and I feel like I can navigate the crowds without hitting folks.
If I'm headed to any of the three other parks and its going to be raining lightly/moderately on and off all day - I might take a poncho - but only wear it if I need to get someplace when the rain is coming down hard and I don't want to get soaked through. I might take an umbrella for between the bus/parking lot and the security check, but it's usually too crowded in the parks. Usually - you can jump between attractions when it's not raining much and really not get too wet. Also, if its raining enough, it can keep the crowd WAY down - and an umbrella isn't bad to deal with. I used it one day at AK, for example, as the park was a bit of a ghost town.
If it's just going to rain all day - both are pointless - you are going to end up wet all the way through anyway. I just wear appropriate clothes and shoes. I might take bag with a change or clothes/shoes/towel and put it in a locker if its going to clear up later or I am headed to a meal at a resort and I want to put on dry clothes or shoes later in the day.
I can't really stand ponchos. While the WDW ones are better than some in that they don't cling as much, you just get as wet from about the waist down as if you were carrying an umbrella and they make definitely increase the humid ick feel you get in the rain!
The hard part about the umbrella - even if YOU are observant about not hitting people as you move forward it - there's just so much stimulation in the parks - folks will still just walk right into it - because they don't even see it - they are looking at something else. You can be leaning on a wall, standing still, out of the way, and a person who is approaching you from behind or the side might run right into it. It's really odd - but I've had it happen enough - I know it's not "my fault."