(i am not so good to write in english, i am surely making a lot of grammar error, so please be compliant with me. I accept suggestions and corrections if you wanna point me where i wrote a "strange phrase" and suggest me the correct way to express myself in the english language)
First impressions:
Shipped from: NEXTORCH K3 http://www.nextorch.com/en/product_detail.php?id=64
and K20 http://www.nextorch.com/en/product_detail.php?id=85

These 2 flashlights are part of the NEXTORCH “S series” and both use batteries with alkaline/NiMH chemistry.
Link to S series http://www.nextorch.com/en/product_type.php?id=4

The first one thing that i noticed once opened the shipping package is their “premium” packaging, indeed it's clear that they're not the classic “cheap” AA/AAA flashlights which can be found on your local supermarkets.
They arrived with included batteries, 1 AA (already installed) for the K20 and 4 AAA (2 already installed + 2 spare), the AA is NEXTORCH branded and came at 1,6v and the AAAs are ENERGIZER branded (expiry date 12-2025) and came at 1,59v.
These flashlights are perfect for personal every day activities but it's almost a sin to use them ...risking to spoil them!
The packaging box is showing all the possible informations and this is a little specifications summary:

• Bulb:CREE® XP-G2 R5 LED
• Lumen:180/70/25 Lumens
• Runtime:26 mins/160 mins/38 hs
• Battery:Two AAAs
• Distance:187'/57m
• Material:Aerospace grade aluminum 6061-T6
• Finish:Hard anodized finish
• Length:150mm x 12.4mm x 13.8mm
• Weight:0.88oz / 25g

• Bulb:CREE® XP-G2 R5 LED
• Lumen:130lm / 6lm / strobe
• Runtime:1h10 min / 150h / 2h20min
• Battery:1*AA(Included)
• Distance:73m / 239.5ft
• Length:82.7mm x 19.1mm x 17.7mm
• Weight:25g/0.88oz(without battery)

Modes and estimated lumens:

Switch type: MECHANICAL for K3 and SLIDE for K20

--- K3 ---
There are “ 4 ” modes in the following order:
Hi – med – low – strobo
Just half press the switch or full press (on/off) the switch to change mode, there's a MEMORY function: hold the preferred mode for at leat 5 seconds and after you turn OFF, you can find the previous setted mode once you turn it ON

My estimated lumens are 200

--- K20 ---
There are “ 3 ” modes in the following order:
Hi – low – strobo
Each time it's turned off and on it does enter the next mode.

My estimated lumens are 130

>>>LIGHT >>> The angle of refraction:

Weight and dimensions measurements (made myself, not by specs):
--- K3 ---
This flashlight weighs precisely 23,8 gr (no batteries)
Height 15,1 cm
Diameter 1,2 cm
Head diameter 1,4 cm

--- K20 ---
This flashlight weighs precisely 23,9 gr (no battery)
Height 8,4 cm
Diameter 1,76 cm
Head diameter 1,9 cm

Construction quality:
As you can see by pictures they use the same high quality black anodization and the feeling in my hand is awesome with a matt rextured body lightly different from other kinds uses in other flashlights.
Of course K3 is a more “premium” item with its stainless steel clip , a nice charming chrome plated press switch and the chrome plated front bezel.

It's hard to tell… both own pros and cons, nothing to complain about the overall quality (that's perfect on both samples), but just about the differences of lenghts, where the K3 is clearly much longer respecting to the K20 which simply use a single battery configuration and can make use of the advantage of being more portable, with a keychain for example.

But if your needs are to use a “slim” flashlight (but long) for medium intense utilizes… the K3 can assure you a sufficient brightness for a night trip throught a small wood, just be sure to bring with you more spares AAAs.
Is the K3 really much more brighter than the K20 ??
Just a bit more, but the use of a classic reflector (instead of a TIR optic on K20) allows you to have a wider spill whereas the center spot is quite comparable.
In addition the COLDER led tint combined with the fact to have about 180 lumens (compared to 130lm of K20) gives to my eyes a real perceived brightnes…. that's simply adeguate and acceptable for every outdoor activity during the night.

The beam on the K20 flashlight is a little more narrower and lacks of an usable spill, but it's normal given the fact that it utilizes a special optic called TIR (total internal reflection).
This optic is widely used on the flashlights which needs to keep the overall lenght as short as possible, and just to mention it's a robust solution very hard to break (almost impossible).

Lanyard hole: NOT PRESENT for K3 and PRESENT for K20

Threads came SLIGHTLY GREASED, but this is not a big con.. it's better to don't use much grease.

Led Tint, reflector and lense:
--- K3 ---
The led is well centered and its tint is cold white.
Reflector made of: ORANGE PEEL – ALUMINUM
Lense made of: GLASS

--- K20 ---
The led is covedred by the TIR optic and its tint is pure/neutral white, tending to warm white.
Reflector made of: TIR optic
Lense made of: PLASTIC