I have also found that the reason my blood sugar is not normal will predict if / how I feel.
If I go high because of a lack of insulin, I will feel really bad. If I go high simply because I ate something with lots of sugar (I love birthday cake) and glucose is getting into my blood faster than the insulin is taking it out, I wont feel any symptoms of being high unless it remains high for an extended period. In this situation though, the insulin usually catches up and brings it down to normal without a correction bolus.
How do I feel when high? Very heavy. Chest sometimes feels tight, like taking a deep breath is not possible. Limbs kinda feel like the blood in them is actually jello thick. Not nice.
On the other hand with lows I find that I will feel bad if the rate at which my blood sugar is dropping is fast. If I've slowly dropped into low territory I will not get the tingly tonge and cold sweats( Yuck!) like I would if I was dropping fast. I could, like has been mentioned, feel low when Im actually still in normal range.
For me, it seems, In both situations I will only feel bad if the situation requires immediate attention. i.e. Low that requires sugar NOW. or high that requires I take a correction bolus.