No favorites, but I use only three positions:
top- about 15%
hoods- about 75%
hooks- about 10%
drops (horizontal ends)- never, except for drying gloves after wet rides
My bars are set well below the saddle height. I use same positions with DT shifters and brifters.

On shorter rides, up to 20-25 miles, probably 80% hoods and 20% drops. Unless I'm fighting the wind, and then I'll spend more time in the drops. For longer distances, I tend to use more hand positions: On the hoods, on the bend just behind the hoods, deep in the drops, the end of the bar...

I suppose I might spend more time in the drops if my bikes had downtube shifters, but I've got brifters and barcons on my road bikes.

I seldom use the tops unless I'm just cruising leisurely. Like with my kids, for example.

I've learned that at my advanced state of decay it's important to keep my hands moving - changing position. That way no numbness, no aches. I suppose I'm on the ramps more than the other positions but I'm on the hoods a lot, the tops and even the drops. It seems like I'm in the drops more than the other riders I see, even the full zoot carbon-a-carbon guys. I'm convinced that the drops help keep my back stretched out so I can ride in the drops. Flexibility. I also ride on low traffic rail trails a lot so I'm less concerned about sudden surprises that demand hard braking. Different out on public roads where I'm very defensive.

I'm in the drops most of the time. Of course I have a reasonable 2.5 inch saddle to bar drop unlike most people today.

Where do I ride? Mostly the metrowest area. When I do it is mostly on the hoods, some on the tops. On the drops only into a stiff wind.

Tops when grinding a long climb if I want more power I move to the hoods. The hoods everywhere else except downhills I go to the drops but if there''s a lot of cornering I go back to the hoods.

On the ramps with my Miyata 912 most of the time, with a mix of hoods and drops to adjust hands and stretch/relax during the ride.
On the ramps with my Voyageur 11.8 or the hoods. Rarely drops- only with a lot of wind.

I am seventy and not as flexible now. On the top 50%, hoods 40% and drops 10% when descending or in stiff wind.

I'm on the ramps most of the time. I also will put my hands on the bend going from the tops into the ramps- spread out the weight distribution as much as possible. Beyond that- the hoods, then the tops.

I really only use the drops going into the wind, or when I want to pretend that I'm going fast.

I use the hand position terms from the Lovey Bicycle! site: Lovely Bicycle!: Drop Bar Hand Positions: an Introduction

Probably about 45% on the hoods, 45% on the tops and the remaining 10% down in the drops

Most of my life, I've spent most of the time on the corners (with my palms facing forward), but nowadays, I live on the tops. I'll be doing some stretching exercises so I can get more comfortable stretching forward and down.

In track races, the rules require you to have your hands in the drops, nowhere else.

pretty much all over the place

This pretty well describes the way I ride drop bars.

Mixed use bike Gen 2 campag

Cruising = Behind the hoods/hoods
Climbing = flats/behind the hoods
Going Down = Hoods
Headwind = Drops
Blown = Flats

City Bike, Friction w Areo Levers
Cruising = Behind the hoods
Climbing = flats
Going Down = Hoods
Headwind = Drops
Blown = Flats

Race bike Gen 1 campag

Cruising = Behind the hoods
Climbing = Hoods (Climbing on big boy gears is hard)
Going Down = Hoods
Headwind = Hoods (i wish i was flexable enough to reach the drops)
Blown = Behind the Hoods

I spend most of my time either on the hoods or the "corners" (the bend just behind the hoods.) I am almost never on the tops, and I only go down in the drops once in a while when the mood strikes. If I had to break it into percentages, I would guesstimate:

50% hoods
45% corners
4% drops
1% tops

I move all over depending on the terrain, wind, motivation, fatigue, etc. I spend most of my time on the hoods, but I have several different hand positions and elbow angles. Sometime I wrap all my fingers around the levers, or put the top of the hood in between middle and index finger, or place the base of my index finger on the hoods. And for go-fast on the hoods mode, I often have my hands on the hoods with my wrists twisted in (elbows at 90 degrees and tight to my chest) and forearms touching the tops. I get just as low like that as when I'm in the drops. Sometimes I'll even ride with just my forearms on the tops near the stem, hands together TT style. Tops when climbing, except of course when climbing out of the saddle. I almost never climb in the drops. (Pantani used to do that a lot, which always confounded me.) I'm in the drops on descents, and when going fast on the flats, especially if I expect that I feel I may need to brake quickly. More likely to be in the hooks when riding in a paceline. If I had to put percentages on it:

tops: 15% (mostly climbing)
hoods: 54%
hooks: 25%
drops: 5%
no hands: 1%

All my riders have STI's
70% - hoods
30% - drops - on long climbs, change up on long rides & descents.
I'm 63 & skinny.