Single-Mindedness is like 'being in the zone' when you are running on a race track, or driving a car, or when you are doing something so repetitive that you are totally engrossed in that activity to the point that you forget yourself, you become absent minded. It's called 'flow' in psychological terms. It's about doing rather than thinking, and this doing rather than thinking brings with it a degree of certainty, and certainty is essential in battle situations because as soon as you doubt yourself you give the enemy an opportunity to strike.
Self-Awareness is the opposite of Single-Mindedness. Self-Awareness is being aware of yourself in relation to other things (be they material things or immaterial things). It means being at calm and being aware of things around you and in you. It's like being on top of a mountain (mount Noos) surveying all things things going on beneath you (on the Plains of Phusis). Sat up here you have the ability to choose how you want to act in the future. You can see the options available to you and then decide how to act. It's this state of mind that the Havamal advises against while in battle because being Self-Aware means you are thinking about 'what ifs' and other possibilities, which tends towards uncertainty.
This is why Single-Mindedness (being Hod like) is better in a battle situation, because you do not succumb to any neurotic seizure which would strip you of the ability to act/fight. Your seizure would cause you to be indecisive and not make the 'killer blow' against your enemy, or even be able to defend yourself. Hence this is why you need to be what the Havamal calls 'blind' (which is not physically blind so that your eyes don't work, but mentally blind so that your brain isn't contemplating the images that it's seeing) in a battle situation, so that you do not 'have a spell' (a psychological attack) cast upon you.
If you want to think about Single-Mindedness and Self-Awareness in a real life situation then you might want to think about a two-man sniper team: a sniper and a spotter. The Sniper is Single-Minded because he is totally focused on the target that he is shooting, He has tunnel vision to such an extent that he is oblivious to all other things going on around him. The Spotter on the other hand IS aware of what is happening all over the horizon. He has Self-Awareness and decides what target the Sniper should shoot at next. This means that he must be aware of options and then choose one. Both men work together and benefit from the partnership.
While the two men in the sniper team may have chosen to be either Single-Minded or Self-Aware, they need not be those roles for their entire life. Indeed they may, certainly will, make use of both states of mind throughout their lives, to their own betterment. Sometimes thinking more, sometimes doing more. Using both states of mind benefits them, and can benefit us also if we choose to do it.
Ráðumk þér Loddfáfnir
en þú ráð nemir
njóta mundu ef þú nemr
þér munu góð ef þú getr
skalattu í orrostu
verða gumna synir
síðr þitt um heilli halir
I advise you, Loddfafnir,
to take advice;
you would benefit, it you took it,
good will come to you, if you accept it:
 you must not  look up
--  the sons of men become
 like men terror-crazed --
lest men cast spells upon you. *