Darrell, they are two very different games. I haven't played Dux Bellorum yet, although I will be playing it very soon.
Basically, Dux Brit is a large scale skirmish game and feels much more 1:1. Your army is about 40 figures and the rules work on a 1:1 basis - one D6 per fig shooting/fighting, single figure casualty removal, etc. I liken it a bit to Triumph and Tragedy: although they are two very different games, the overall 'feel' in terms of game scale is about similar.
Dux Bellorum is element based and each unit (element) = about 50 men. The number of figs per base is up to the player. Each element has a cohesion score, so no individual figs are removed as casualties and each element throws set attacke dice etc dependent on troop quailty. So it feels more 'large scale battle'. In practice most armies have 7-10 units so about 300-500 men per army, which is quite large scale for the period. I'm told it plays really fast and games can be over in short order!
I'll post a review on my blog once I have played. The first game I have will be using our Hail Caesar sized units on 160mm wide bases just to put loads of figs on the table 18-24 foot, 12 cavalry, 8-10 mtd and foot skirmishers per base) and using a 4" standard measure (the game uses 'base widths' as measures in the rules, but that limits the number of models at 28mm scale and we want to use all our toys!! This is also me with an eye on how the game might be displayed at a show where spectacle is important!) I also have 120x80mm sabot bases built to accomdate smaller forces for typical club games - 4 cavalry, 10-15 infantry, 3 mtd skirmishers, 4 foot skirmishers per base.
Like I say, keep an eye on the blog for more details.
However, for sheer fun factor, you can't beat Dux Britanniarum - I can't recommend it highly enough!!
Andy