Technically kelvin and lumens are two different things. Kelvin is a color/temp range and lumens is output brightness. The loosely used rule of thumb is that a 4300k bulb puts out appx 3200 lumens while a 6000k bulb puts out about 2800 lumens. This can change dependent on bulbs and manufacturers. As an example, the Philips D25 85122+ (4300k OEM-style bulb) has an estimated 3200 lumens from Philips while their Ultinon D2S 6000k bulb is rated at appx 2400 lumens. So, if you went from 4300k OEM Philips bulbs to their 6000k ultinon then you would actually lose 1600 lumens (800 per bulb, 1600 for the pair). Obviously that is less light output. Yes, the color of the bulbs would be more white than the yellow hue of the 4300k.
Now, with that being said, the human eye sees certain colors better than others (
http://en.wikipedia.org/wiki/Color_vision). Reds have the widest wavelength of color, followed by greens and blues. The wiki link shows blue/violet has the shortest wavelength while yellow/red is the widest range. BUT, from a brightness sensitivity perspective the greens and yellows seem to be the best.
So, with HID bulbs at least, you do get less lumens from the higher kelvin color ranges. There is also issues that involve color due to eye sensitivity and wavelength. 6000k bulbs have a whiter light to them but less lumens than the 4300k (which has a yellow hue), thus, 4300k actually put out the most light in comparison. 10000k and 12000k put more of a blue/violet light out, have less lumens output as tested (depending on the bulb/ballast, etc) against their similar counterparts, and the color shift to the blue/violet range is the worse from a sensitivity perspective.
I like my 6000k range. To me the whiter/slight blue hue picks up the white road stripes better on the highway. I've had 5000k HID in the wifes car that had a green/yellowish hue and didn't really care for it much. I saw OK but the color green was kinda crappy looking from a style/visual perspective.
Tinting the headlights will change the color range of light coming out of the bulbs. To what, I don't know. If upgraded to 6000k then I would think you'd have FAR less light output due to the 6000k light output AND less light being allowed through the tint. With my 6000k I feel at times I need more light and I would hate to drive in the rain in a car with tinted headlights.