I was on Lantus first and changed to Levemir. I prefer Levemir, although not a pure comparison because on Lantus I hadn't done DAFNE.
The longer duration of Lantus is marketed as an advantage, but may be counterproductive if you need different basal doses in the day compared with the night. You could end up choosing between being high one half of the 24 hours, or being hypo the other half. Although DAFNE can help correct highs/lows, it works best if your basal is set right. That is, not having your basal artificially low/high and doing constant corrections for highs/lows at regular times.
In your shoes I'd try DAFNE first, then if necessary try another insulin. You'll gain from the feeling of freedom from doing DAFNE anyway. If all else fails consider a pump so you can set the basal rate to change when you need it to avoid the morning highs.