AlexGT,
Brightness, as a practical matter, is really subjective. The stock KL1 runs at 350mA stock.
Mr. Bulk, chime in if lux readings show otherwise. I don't have a lux meter.
Let's just use a 1W as an example since those are what you mentioned. If you increase the current 100% and go to 700mA, you'll get about 50% more light. It is noticeably brighter and I wouldn't have it any other way. The KL1 will run fine for long periods at 700mA. It can handle this heat.
If you go to one amp, the increase in brightness will be marginal. The reason being the law of diminishing returns, for lack of a better term. As you increase current over 700mA you'll get less of an increase in brightness, but a lot more heat. The batts in a 2X123 configuration will also have a really hard time keeping up with the demand of the circuit and LED at this current. That's why you'll only get around 1 hour of runtime at 1A as opposed to two hours at 700mA.
If you want a good practical light, a KL1 at 700mA driving a nice low Vf high dome with a Fraen LP is the way to go. It's a very cost effective mod and this sucker will THROW. If you're in a situation where the extra light provided by 1A will make a difference, you should have brought a bigger light with you.
As far as going to one amp goes, it is a very bright light, but you really need the right host for it. The KL4 can get by running at 1A because it has more meat by virtue of the mass around the reflector. The KL1 is just a shell. I've sold a few 1A KL1 mods and they are nice. Those that got them like them, but for what they are. INSANE.
If you're interested in something like this, CM does these mods, as do I. PM with questions before you take the plunge. If you like the color of the recent 3W LEDs that have hit the scene, you might want to check those out. I haven't found them to be any brighter, subjectively (Go ahead Charlie, hit me!), but running one of those at 700mA or even 1A would not be overdriving them, but running them to spec.