Based on my study of Buddhist texts, the guidance of my teachers, and my own experience - the most effective meditation (of this type) is to maintain awareness of the entire breath AND feelings, while releasing any mental/emotional blocks that you notice thanks to this awareness.
First of all, there is no magic in merely holding your attention - whether it is the tip of the nose or the diaphragm or abdomen or anything else. There is no magic button somewhere that will open some door if only you keep pushing, nothing like that.
Instead the key principle is to stop creating/maintaining trouble in your mental continuum. This is called "samatha". In order to stop creating/maintaining trouble we must notice it first. This is called "vipashyana". The better you see, the better you stop, the better you see.
When you watch the entire "body" of your inner experience, it is likely dominated by thoughts. This is expected in this era. There is another type of meditation for working with thoughts. But for this meditation you need to tune your awareness to predominantly watch everything but thoughts. This includes sensations of the body, the somatic components of emotions (the part of emotions felt in and around the body), and the emotional aspect of your mindstate (colloquially known as "the mood"). Sensations of the body include the muscle tonus, posture, and any acute neuroses manifesting in body shaking, tensions, or blocks. In the very center of this entire body of non-discursive experience is the cluster of sensations connected with breathing.
The breathing sits right on the intersection between physical and mental, which is what makes it special. If you center your awareness on the breathing, you will naturally include most of the bodily sensations on one side and most of the emotional aspect on the other side. This makes breathing a perfect focal point.
Specifically, it is the muscles involved in breathing in and breathing out. Because, if you watch carefully, you will notice that these muscles are extremely sensitive to all emotions. Any change in emotional "weather" results in the change of tension and affects the speed with which these muscles contract and relax. So by watching the state of muscles connected with breathing you can very clearly see your emotional state.
Once you learn to see the emotional state, you don't really have to focus on breathing. The point of all this exercise is not breathing, after all, it is perfection of samtha and vipashyana.
So the entire exercise of meditation is to watch all that, and to trace these blocks and neuroses to their emotional roots, so you can uproot them. This process of tracing may involve a little bit of thinking, but for the most part your job is to dwell on the feelings. The hangups are something you discover by seeing, not by reasoning.
Once you see them, you let them go, release them, dismiss them - whatever you want to call it. As said in the sutta, you watch your breathing in long, you watch your breathing out long, you watch your breathing in short, you watch your breathing out short, you watch your breathing while paying attention to the whole experience, you watch your breathing while relaxing the mind, you watch your breathing while gladdening the mind, you watch your breathing while liberating the mind.
This is not all there is to Buddhist meditation, and not all there is to Buddhism - but this is a big chunk. Just practicing this for a while (months? years?) will be of great benefit to most anyone.