An ultra-wide-angle zoom lens is one of the most used lenses in most kits and that means Canon having a high-performing 16-35mm lens in their lineup is a big deal. That we get to choose between two incredible L-class options or, better yet, include both in our kits is an even bigger deal. Either way, there is a choice to be made, either at purchase time or at select-for-use time.
For lens selection, image quality typically has very high importance and in this comparison, both lenses are performing very impressively with the III delivering slightly better image quality at f/2.8 than the f/4L IS does at f/4. Stopped down, I don't see image quality factoring into this decision process.
The significant differentiators are that the f/2.8 L III lens has a twice-as-wide max aperture, a roughly twice-as-high price tag and is lacking the image stabilization feature.
The wider aperture means that subject motion can be stopped in lower light levels with faster shutter speeds and/or lower ISO settings being used. A wider aperture means that a shallower depth of field is available and a stronger background blur can be created. Wide-angle focal lengths are not optimal for creating blurred backgrounds, but there is still a difference between f/2.8 and f/4 in this regard. When used at narrow apertures, wide aperture lenses will typically create larger starburst effects from bright lights than narrower max-aperture lenses. While there are many that do not care about this difference, it is a significant decision factor for some of us.
Make the aperture twice as wide and the lens elements and package holding them need to be scaled-up similarly. An f/2.8 lens typically has a larger size and heavier weight than an f/4 lens. In this case, the Canon EF 16-35mm f/2.8L III vs. EF 16-35mm f/4L IS USM Lens specs comparison shows the f/2.8 III weighing a modest 6 oz (175g) heavier (27.9 vs. 21.7 oz / 790 vs. 615g) and measuring a bit larger, 3.5 x 5.0" vs. 3.3 x 4.4" (88.5 x 127.5mm vs. 82.6 x 112.8mm). The larger size means that the f/2.8L III has larger filter threads — 82mm vs. 77mm.
The increased cost factor is directly related to the increased size of the lens elements and other parts and the aperture opening size-difference-to-price-ratio holds solid.
When shooting from a solid tripod, image stabilization typically has no realized benefit in this class of lens. When the tripod needs to be left behind, for convenience, for comfort, for shooting speed reasons, etc., image stabilization can quickly become far more important than a wide aperture. The f/4L IS lens' 4-stop image stabilization system significantly surpasses the 1-stop aperture difference when shooting handheld and not trying to freeze fast subject motion, giving the IS lens a great versatility advantage.
Making the Decision
If your budget does not reach to the f/2.8L III, your decision is made. Get the f/4L IS lens. It is awesome and few will regret buying it.
If sports action and low light events are on your photography list, the f/2.8L III lens is the right option. The same option should be selected when the maximum background blur is desired.
If leaving the tripod behind, the f/4L IS is usually going to be the right option. Those carrying a lens a significant amount of time, such as when backpacking, will appreciate the f/4L IS' modestly lighter weight and smaller size.
Those interested in photographing the night sky, a form of action photography, will definitely want the f/2.8L III lens as will those looking to create the biggest stars from point light sources, a common desire for cityscape photography during the blue hour or after dark. Otherwise, the f/4L IS is going to serve most landscape photographers perfectly.
Those who want the absolute best image quality should opt for the f/2.8L III.
Having both of these lenses is, of course, the ultimate option, but again, the decision regarding which to select for use must still be made.
More Information
Canon EF 16-35mm f/2.8L III USM Lens Review
Canon EF 16-35mm f/4L IS USM Lens Review
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Canon EF 16-35mm f/2.8L III USM Lens: B&H | Adorama | Amazon US | WEX | Lensrentals
Canon EF 16-35mm f/4L IS USM Lens: B&H | Adorama | Amazon US | WEX | Lensrentals