Mr Bowie,
Keep in mind that you asked a very open ended question. Also, HI has a sub-forum here in Blade Forums so you are likely to run into lots of their followers. Also, there are far more than one Khukuri House.
The kukri is basically a hammered piece of spring steel with a wood or horn handle glued or pinned to it. If by "best" you are asking about looks, then I don't think many would argue that HI would win. Their fit and finish is second to none. But I will add that if you get an ornamental kukri from one of the khukuri houses they also make some very nice lookers.
If by "best" you mean accuracy of the traditional models, once again HI would probably win hands down. And I say that even though HI does make some adjustments to the measurements for larger western hands and they do have some non-traditional models and hybrids. But if you look at the khukuri house websites and look at their "traditional village" models you will find most of them falling into the currently popular size of a 10.5 inch blade. The real traditional village models are purpose built and as such, vary greatly in size and shape to do that particular job. That is not reflected in most of the Houses but you can find that with HI. Some of the better Houses do offer different sizes within a particular model and many will make you whatever you want.
If by "best" you mean the best at work then its a closer race, but even then I think you will find that HI is going to win out. In the working category there are several important issues that may be different from production knives most on this forum are familiar with. Important issues are the shape, size and weight of the blade and the quality of the hardening of the blade. This is important because every kukri is not meant to do the same job and some simply cannot do the same jobs. For instance, if you order a Sirupate for heavy camp work you will be dissapointed and may break it. If you buy a heavy village chopper for hiking you would be similiarly unhappy! That does not mean it was a bad kukri, it was just used for a purpose it was not designed for. When you throw in the fact that some of the Khukuri Houses put out "Tourist Grade" products, basically souvineres, they are not meant for real use and will fail. So for the blade part, picking the correct model is important as is the size, shape, weight of the blade and quality of the metal. Bigger is not better. Heavier is not better. Thicker is not better. Usually, "correct" is better. The traditional designs have been developed over hundreds of years of trial and error and they now exist because they have stood up to the test of time, through hard work.
Another important part of the kukri is the handle. In Nepal a kukri may be passed down from father to son, or more accurately, the blade may be passed down from father to son. They may take that kukri back to the local blacksmith from time to time to get a new handle and touch things up. Something we hardly have access to in western society. Remember, the kukri is a farm tool there and gets regular daily use so in one year it may see more duty than two lifetimes from a weekend camper.
Lastly is the scabbard. Here you will find that Hi consistently puts out a better product. Better leather and much more attention to detail.
Many on this forum have kukri's from both places, myself included. I love them all. (OK most of them) And most will do a reasonable amount of work, usually far exceding what the average person will expect of it. And most of the good Khukuri Houses will replace a substandard blade unless it is abused. At least for a period of time following the purchase. I highly doubt that many would replace a blade after a few years of use like Hi will, but even with HI, that is as long as it wasn't abused and asked to do jobs it was not intended for.
Either way you go, be sure to email who ever you buy from and let them know you want a user and tell them what you plan to do. They will usually spit out a few models that will do the job and that will give you some choice of different looking models. By telling them you want a user you will usually take a tourist model out of the mix. None of the companies want pissed off customers so "most" will not try to slip in a tourist model if you communicate that you will use it hard. Good luck on your search.