There is a fair amount of debate on the WotC boards on how much dragonmarked houses compete. Some feel that with no central government; pricefixing, bid rigging, and other forms of collusion would be the norm. Others feel that those who would cheat their customers would also try to cheat the other houses (or other members of their own house) for personal gain. I feel that individuals will feel grudges of deals that did not work out well for them, and over time will develop into fierce competion.
House Vadalis does not compete with any other houses, but with the Ashbound Druids & the Elves of Valenar against them, they don't need more problems.
House Lyrandar and House Orien compete over transport/commerse issues. (Including transporting dragonshards out of the Shadow Marshes; currently House Tharashk who mines the dragonshards, has an alliance with House Lyrandar.)
House Phiarlan and House Thuranni compete, over... performance venues, right, that's it, performance venues. While House Sivis deals in information, and doesn't seem to compete with anybody. Although both House Orien & House Vadalis maintain messenger services, but I definately don't see any elven houses intested in information.
House Kundarak and House Medani compete over security work (small scale). So would not in any way come into conflict with elven "entertainers". No conflict there.
If you want troops (large scale security) then they are provided by either, House Deneith (Standard Race Troops) or House Tharashk (Monsterous Humaniod Troops, typically from Droaam). Of couse, during the war House Cannith started providing troops (Warforged) also. I bet House Deneith is glad that nobody is making warforged any more. Because if someone was making more warforged, then it could be a threat to House Deneith. But they're not making warforged anymore. Nope, no more warforged.
Of course House Ghallanda and House Jorasco have pratical monopolies, with no serious competition, so they could probably take over all of Khorvaire, and eventually all of Eberron, if they weren't halflings.