Load your bag or Load your bike
If the road is so harsh you must stand up to manoeuver (off road, back country, XC, etc.), load yoursel Pandora Charms f. The bike suffers less (tires specially), and you can avoid falling from lost control;
If you have lots of gear and proper tires, loading the bike help to ride more stable and comfortable, since the cushioning effect of the tires (suspension) is enhanced by the added bicycle mass;
If you ride short, loading back is much more pratical. But if you are touring, loading the back becomes a huge source of discomfort and even health problems.
Tire choice is important, also. On a skinny tire road bike, I would not feel safe or comfortable to put a rear rack in nothing but the smoothest of paved roads. In the other hand, I have already made loaded touring in roads that looked like the moon surface. How much is too skinny, or fat enough, depends on each person/bicycle/road.
In the end, the answer is “it depends”, but I think the three (four?) parameters mentioned here are the most important about “what” it depends on, IMO.
I think it depends. From personal experience, after you learn to use
Generally, for better handling, it’s best to keep weight as low on the bike as possible. And whether distributed front or rear makes little difference on (non technical) uphills (though some tourists feel that having weight in front panniers actually improves stability on downhills and rough roads, so long as the weight is well secured and can’t flop around).
[On reflection, I can see that a loaded backpack might noticeably improve climbing or accelerating while standing, since the backpack weight would place more weight on the pedals.]
In warm weather or for long rides, the backpack inhibits cooling and collects sweat.
However, there is a major convenience factor to the backpack in that you can easily take the stuff with you when you dismount the bike.
(Note that you should never put any substantial weight in a handlebar bag they are universally too poorly secured and flop around, impairing handling. Weight in a seat bag should be well secured with cinch straps around the bulk of the bag.)
As has been implied, it depends. I rode from Pittsburgh to DC on the GAP and C this past summer. On my touring bike, with 700×32 tires as much as possible was in front and rear panniers mounted as low as possible. The bike was stable and I was comfortable with a fanny pack when off the bike for meals, etc. When I commute to work I have a bike messenger bag I can use when riding my touring bike or road bike (with 700×23 tires). If I have a lot to get to Pandora Charms work I will use the touring bike with panniers, usually rear. I feel more comfortable, especially on a warm day, if I can put the weight directly on the bike and not on the bike through me. The mechanics of carrying weight on you make it more difficult to stay upright if you hit a bad bump or pot hole as you have to combat not just the weight of the bike but also the mass (notice I said mass, not weight) that wants to pull you from the vertical with a wider swing. I also notice the weight more when it is on me rather than on the bike directly.
Commuting on the commuter bike Water bottles in the bottle cages. Repair kit in a seat bag. Work stuff in the pannier(s); but at times a pack.
Road bike ride on the road bike Water bottles in the bottle cages. Repair kit in a seat bag. Food and misc in the jersey pocket. And in hot weather and/or in remote areas, sometimes additional water in a Camelback Razor hydration pack.
Quick errands on either bike Usually a backpack or messenger bag. Especially if I’m getting on and off the bike a lot and don’t want to deal with the panniers.
Grocery shopping on the commuter bike Pannier(s) and at times a backpack as well for an extra big load.
Mtn biking on trails Water bottles in the bottle cages. Repair kit in a seat bag. Other stuff in a pack and/or jersey pockets. (Panniers are too liable to catch on obstructions.)