I have tents, tarps, bivvies, et al. My time spent outdoors has ranged from sleeping in wet clothing under trees in pouring rain, all the way up to an outfitters camp. If I am carrying it, and know the terrain/area, I will go with my tarp/hammock setup every time. Sleeping is SO much more comfortable. Places with no trees, a tent. But, far and away, I am a hammock convert. Tarp just sorta follows suit

In the Sierras in summer, I carry a bivy and a tap, but never use them. I carry and use my ultralight tent for one reason only - bugs.

A well rigged tarp is often more pleasant than a tent in the rain, but a slightly sturdier mountaineering type tent can't be beat in really nasty, stormy weather.

I'm thinking of getting a Hilleberg Bivanorak

I too use a lightweight tent (Big Agnes SL1 - under 3 lbs) because of mosquitoes. I've been in places where you would go absolutely batty in 30 minutes after the sun sets. Some people resort to a bivy bag with a hood and netting. The ultra-lighters (sub 15 lb packs) generally eschew even a lightweight tent in favour of a tarp and so they save the final few oz. That said, I do carry a lightweight tarp (6'x8' 9 oz. silnylon) for day trips or to provide extra coverage (over the camp kitchen). I have yet to be in a place where bugs are not a problem (even the relatively mosquito free Rockies).

But in my humble opinion, if you don't have a peaceful restful night of sleep with bug protection and a decent thickness pad under your sleeping bag, then you are just giving up a lot of NECESSARY comfort. As Mors Korchanski taught us - if you get a good nights sleep, you are better able to cope in a survival situation. Comfort during sleep is not a luxury, it is a really good survival coping strategy.

Although I've never tried one, a version of the Hennesy Hammock looks like interesting solution.

On a side note, comfort is a relative thing. It's important to keep in mind that whether you pick a tent or a tarp, it's only part of a bigger system. How comfortable you'll sleep during the night depends on a few other factors, especially your sleeping pad and ground insulation.

One reason why I like my poncho lean-to setup is that it allows me to pile up lots of insulation underneath, which makes sleeping a lot more comfortable. Usually small spruce branches arranged like roof tiles about a foot high or a similar thickness of dry leaves covered with a thick layer of moss. On top of it a closed-cell foam pad and my sleeping bag. IME, that setup beats a tent and a plain sleeping pad any time in terms of comfort. It takes me about 30 minutes to make that kind of shelter with a knife or axe. Not much longer than it takes to set up a tent.

I've slept a good many nights under a poncho, anywhere from the mountains to the seaside (even in a swampy valley in the middle of the Scottish highlands once lol), in heavy rain and at temperatures down to freezing. It did get cold in my sleeping bag on a few occasions, though never unbearably so, and not once did my lean-to leak in the rain. So it's definitely a feasible alternative in the bush though it's not for everyone.

A bough bed is great but I always struggle with the LNT ethos when it comes to that. A good deal of the time I might be in a national or provincial park where cutting boughs would be a no no. Outside of parks and in Canadian boreal forest it's probably OK but I still feel a bit of a guilty pain when I start stripping trees for boughs even if it just the lower 6'. Hmm, maybe I just need to get over it?

And I am often in simple mixed forest parkland of birch and poplar or I am in the basic prairie - for me there is only way to go.
I.e. the tent or a tarp with a netting which combined is basically the same weight as the tent and 2x as long to set up.

I basically discount the contained heat advantage of the shelter, as a tent may only be a degree or two warmer than the surrounding air. For some reason people have this silly idea that a tent is there so that you can put a heater in it and keep you warm! Silly concept I'd say. If your bag/pad doesn't keep you warm, you could use extra clothing. And if that isn't sufficient then you brought the wrong bag!
The biggest thing about a shelter for me is to block the wind which will make you feeler much cooler than the surrounding air. A couple years ago, I was out with a group of lesser experienced people. One guy who hit the sack early had buttoned up the tent tight so that it wouldn't ventilate and then complained about his bag getting moist. The next night we opened all the vents and were dry and warm. He did not understand that a tent needs to breathe and should not be shuttered tight for it to work properly.

"Comfort is relative." Couldn't agree more - for me I like my 1.5" inflatable pad and -12*C bag. Although I've used the 0*C bag in temps as low as -8*C by wearing my extra clothes. I also build a pillow / neck rest from clothes and ditty bags. Some people can get by with a simple 3/8" x 3/4 length foamy on hard ground and use a quilt!

It is also quite normal to wake up a few times in the middle of the night to roll over or adjust your sleeping position. To sleep through an entire night without doing so is a pipe dream for me - I simply have to move about.

Some people like the visual "privacy" of a tent or think that it will eliminate the sound of people talking from the next tent. I'm not sure where they get that idea from.

Most lightweight tents are mesh inners, with the fly being the weatherproof part. This eliminates the need to vent the tent (in the higher end models anyway). That being said, Roarmeister is correct; the temp difference is mostly due to the wind being eliminated by the nylon tent barrier. With a tarp, you do not have this. Even pitching it side into the wind, there is still convection happening; hence, the need for quality bedding & sleeping bags, as these are what keep you warm. Losing heat to the wind, or the ground, is more prevalent in a tarp than a tent (well, to the wind anyway-ground is still dependent on what you are sleeping on, for the most part).
My setup 95% of the time is a silnylon tarp, with my HH exped hammock, the underpad, and an AMK heatsheet. The heatsheet goes under the foam pad, which goes under me. It provides some radiant heat reflection, as well as being a windproof barrier underneath me. The setup hasnt failed me yet. The best part about having the tarp is that I am not concerned about spilling food on the floor when its pouring out . I live in a no bear area, so, bears arent a concern!

I'd take a quality tent over a trap 100% of the time. You can always take the fly off the tent for better air flow and vision in hot weather, and the tent is warmer in winter. Tents keep one free (mostly) of insects and crawly things. Just my personal opinion.

I've no experience with a hammock, but have started thinking I'd like to get one to try out.
I have spent many nights, and long rainy or snowy days, in various tents and under tarps and ponchos set in various patterns. I greatly prefer the tent. They are much better at keeping weather and bugs and other crawlies, snakes and skunks, out. The difference in weight is negligible and worth it to obtain a comfortable night's sleep. When operating in extreme conditions, say elk hunting in the late season in Colorado Rockies, or quail hunting in the Arizona desert, the need for good quality sleep cannot be overstated.
When comparing tents and hammocks or tarps, I find little need to include the sleeping bag and pad, as they will be used with either type of shelter. The need to insulate under the sleeping bag is the same with a tent as with a tarp, and I suppose as with a hammock.

Hennessy Hammocks is making a new type, one that has a side-zip, as opposed to the birth-canal like entry (as it is often referrred to). Although the bottom entry is great, some, like me, had their hammocks modified for side entry. the upsides of using a hammock are site selection (as long as you have anchor points, you have a campsite), ease of setup (once you have a system down, it typically takes about a minute), setting up out of the weather (I ALWAYS set the tarp up first, so I have a nice, dry place, out of the sun, to set up the hammock), and comfort (nothing digging in to me). Barring any camping in the winter (which I no longer really do), my tarp/hammock combo will be my main go-to for any & all overnights, so long as I can find 2 places to tie off.

Sorry guys, but I need a tent. The weather and bugs here are not very "tarp friendly" except in a emergency situation.
My go-to tent when I'm alone is a simple Eureka Timberline 2. Rock solid A-frame tent that can handle the weather. And it won't break the bank to buy one.