The images from this lens are very sharp, contrasty and show a lot of details even in wide open at f/2. The depth of field is very shallow at f/2. As a result, the background will be compressed.
Because of that features, Canon 135mm is ideal for portrait, especially candid portrait, street photography and indoor sports.
Build quality is very good, the best Canon can made. The lens is not as big and heavy as telephoto zoom.
But unfortunately, this lens does not have Image Stabilization built-in. Image stabilization in telephoto is quite important so you can shoot with shutter speed lower than the focal length X crop multiplier. For example, when you attach this lens into crop sensor camera such as Canon Rebel series or 0XD series, then you need to set a shutter speed to at least 1/200 or greater to get a tack sharp result. It is also depend on how steady your hand is. If you have steady hand, then 1/160 will be adequate.
This lens have a decent closing focus (1m) this is better than most of the telephoto zoom range. You can also get a extension tube to get the focusing even closer (.6m with 2x extension tube).
Therefore, this lens will be quite good for macro photography.
The application of the lens will be quiet narrow. Candid photography is one in my mind when I think about this lens. It is because the telephoto range, maximum aperture, and the size is not that big and obtrusive.
The second one will be close-up and head-shoulder portraiture, and then for indoor sports such as volleyball, basketball and so on.
This lens does not have a wide range of application because the inflexibility of fixed focal length lens (prime lens).
Although the focusing is quite fast, but it is not as fast as EF 50mm f/1.4 USM or EF 85mm f/1.8 USM. So in the fast action sport, expect to miss some shots.
They are similar in price. the 70-200mm f/2.8 has more flexibility but bigger. The 70-200 f/4 L IS is great because it has IS but you don’t have the luxury of big aperture. The weight of f4L lens is almost the same, but the length is slightly longer.
You will love this lens if you are into close-up portrait, candid photography and indoor sports shooters. With extension tube, you can transform this lens into a super sharp macro lens.
Is it worth it? This lens has a narrow application, so if you are specialized in candid portraiture or indoor sports and want the sharpest lens. This lens is definitely for you.
If you are looking for more versatile lens, then investing on high quality telephoto zoom lens will be better.
Travel and general purpose : *
Landscape : *
Portrait/Still Life : ****
Candid/Photojournalism : ***