For Competition organisers, there are broadly three choices (I'm sure everyone will now come up with loads more!). These are:-
1. Fully Open
2. Pick a specific, tight, historical theme e.g. Italian Wars, TYW, ECW, Early Ottoman Expansion, Wars in India etc. These can be tightly set such as Italian Wars in Western Europe, or armies of the far east. The later works because of the commonality of the troop types available to army choices.
3. Pick a specific date or range of dates, say 1560 or 1628 -1658, and then any army, any book legal on that date (call this a loose open)
They each have their pro's and con's and there is, I believe, a place for them all
1. Allows the widest choice of armies and ensures that any player would be able to field an army. However, these can be a bit "Scissors, Paper, Stone" and very draw dependent. In the Renaissance era, with the steady development of more modern and efficient weaponry, this has seen a move in fully open competitions to armies being chosen predominately from the later European armies post 1635 chosen from Duty and Glory and Wars of Religion. At this years Britcon, there wasn't a single army from Trade and Treachery and only 1 each from Clash of Empires and Cities of Gold and 4 from Colonies and Conquest with the other 19 coming from the later books.
2. These tend to be, IMHO, the most fun games to play! Historical opponents with similar troop types with often subtle differences which really make for some fun and tight games. Two of my favourite competitions this year were from the FOGR Southern league and featured Italian Wars and Early Ottoman Expansion. This option is also the one that the rules best handle! All the debates raging on these forums about relative points costs etc. disappear because everyone is using roughly the same. This is when Polish Hussars come into their own as in the later period they will not be fighting HA Pistol/Pistol Cuirassiers as by then these have been phased out. Interestingly these themes seen to attract the widest variety of armies as often there is no obvious "killer" army! If I reflect on this years Roll Call, out of 16 entrants there were 14 different armies and the Clevedon round of the Southern league featuring Eastern armies had 14 different armies out of 24 with 6 of the duplicates being Moghals!
3. These are probably the most common form of competition choice as they offer both the benefits and drawbacks of options 1 and 2.
For myself, I am happy to enter any competition but do prefer to play number 2 (tight themes - where else could I field my Hawaiians?!

) followed by 3 and then lastly fully open. Certainly fully open themes give me the most agony in choosing a list because of the "Scissors, Paper, Stone" effect and this tends to drive entrants to more homogenous, vanilla army lists
The great thing about the UK scene now is that we have a large number of competitions, catering to all theme genres. Britcon and the 25mm comps are open, the FOGR Southern leagues and Campaign are tightly themed and most other events are a variety of loose opens! We are seeing ever greater innovation from Competition organisers at the moment with lots of new things being tried such as the specific date approach first used at the Doubles this weekend, the innovation at Godendag next January that sees armies from FOG A&M being available and the Mediterranean theme at Devizes which gave entrants the "best of a bad bunch" choice! There are others we have not yet tried such as "Average Joe's"; ratio'd lists (i.e. max 75% inf, 35% Cavalry 15% Artillery 10% Other) plus many more.
However one thing holds true - Long may it continue!!!
Don