I have used both, but not at the same time. It is easier to organize with panniers in my opinion. I used the BoB Ibex trailer on the C&O and the GAP and no matter how careful I was in packing the trailer bag, things tended to shift and settle, with the heavier stuff working it's way to the bottom. I traveled with my wife and it was our first trip so I had the gear for two. We had to camp a few nights and when we got to camp i needed to completely unload the trailer bag to find the tent and sleeping gear, etc. That was a pain when it was raining. The weight is pretty much an even trade off. The trailer weighs in around 18 pounds. I ride a Surly Disc Trucker and use their chromoly racks which add about 7 pounds with front and rear combined. I also have Ortlieb panniers that weigh in at 4.2 pounds for the rear and 3.5 pounds for the front. So racks and panniers add about 15 pounds and the trailer adds 18. There are lighter racks and maybe panniers, but Ortlieb panniers are the best you can buy in my opinion.
I found the panniers were also easier to access when riding. I keep my rain/warm gear in the front right and can get at it without dismounting. Also in bear country I have a separate pannier for food and bear-bagging stuff. I found it easier to over load the trailer as well. On the plus side for the trailer, the weight is distributed over a 5th wheel which I have to assume reduced overall drag but never researched that. Another thing with the trailer is that I took it shopping and was able to throw 2 bundles of firewood on the trailer to bring back to the campsite.

As far as handling it some ways the trailer handled better. A few times I had my panniers unbalanced and hit a scary shimmy at 18 mph, got past that only to hit a worse one at 24 mph. Never really had a bad shimmy on the trailer but people do complain about that. I did have a trailer crash when I was hauling at about 18 to 20 mph on the C&O trying to get to a campsite. I was passing through a partially closed gate and glanced over my shoulder to look for the campsite. The tip of my handlebar clipped the gate and the forward momentum of the trailer pushed me into a bad skid and we had a yard sale. Minor scrapes since it was dirt.
We now travel with panniers and split the gear between us, but 4 panniers for a 10 day trip might be overkill. The other odd thing that I noticed from the backpacking side of my life is that thru-hikers (I thru-hiked the AT in 2007) carry less weight that weekend or section hikers. I started a cross-country bike trip which I did not complete, but I also over packed. I should have know better from my backpacking experience. However, living in the woods on the AT, and going into trail towns, you can get away with being a little less hygienic or dressed in a ratty outfit. I hiked with boots and crocs 2 pairs of shorts, 2 t-shirts and rain gear. I wore crocs in town and threw on rain gear to wash my clothes. When I set out on my cross-country bike trip I packed town clothes and town shoes, etc. to not offend the general public. Next time I will skip all of that. Plus food is way easier to find on most bike routes, as is water. You think that you can ship back what you don't need, but on a long-distance bike trip you are better off to start without it and buy it later if you really need it. Biking brings you past shopping areas almost daily and now there is Amazon that would ship to you next hotel or hostel.
Hope this helps, safe travels.