I now own the 70-200mm f/4L IS lens...
My first "L" tele-zoom was the 70-200mm f/4L non-IS model. I found that this was an excellent lens as far as build and IQ but, that is was not as versatile as I would have wished. I needed a LOT of light or a high ISO to be able to hand hold this lens.
I didn't have a LOT of light all the time - even here in Sunny San Diego County, California we have frequent (especially during the "June Gloom" time) heavily overcast days. Additionally, I want to shoot in shaded area or during early morning of late afternoon times.
Raising the ISO was O.K., but I didn't really like to shoot at a high ISO generally and when I shared a body with another lens, I would frequently find myself switching ISO which was a royal pain.
I craved for IS capability but, at first there were very few choices available.
The 75-300mm IS lens did not have the IQ I required.
The 70-300mm IS DO lens did not provide (IMO) good enough IQ to justify the high price.
I rented the 70-200mm f/2.8L IS lens and found it to be heavier than I desired and larger in size than I wanted. The price was also pretty high.
Canon then introduced the neat 70-300mm f/4-5.6 IS lens and I decided to wait to purchase that lens because it originally had focus problems at 200-300mm in the portrait position. The front element also rotated while focusing making it inconvenient to use a CPL (however, I could have lived with this). At first, Canon refused to even acknowledge that there might be a problem with this lens and then recalled them for a fix.
Before the 70-300mm f/4-5.6 IS lens reappeared on distributors shelves, Canon unexpectedly (to me at least) introduced the lens that I really wanted: the 70-200mm f/4L IS which (IMO) is one of the greatest lenses that Canon offers. I purchased one of these fine lenses and I have been absolutely happy since.
The IQ is amazing even wide open and even paired with a 1.4x TC (which gives me an equivalent 448mm focal length.) It is relatively light for a lens of this focal range, yet its build is sturdy (as is the build of every "L" lens I have used). It is weatherproofed (even though my 1.6x bodies are not). Its AF is fast and snappy.
It is not really great in one area, minimum focus at 200mm. However, I seldom will use this lens at that F/L and focus distance.
The IS on this lens is simply wonderful. I am an older gent who doesn't have the rock-solid hold that I did in my younger days. Never-the-less, I can get virtually 100% keepers (regarding sharpness from lack of camera movement) using 200mm at 1/60 second and I can get a very respectable percentage of sharp shots using 1/30 second at that focal length.
I carry this lens with me everywhere in a top loading holster case with a wrist strap connected to the body. I use this lens so often now (3-4x more than the older non-IS model) that I have dedicated its own body to it,
It is fast becoming my favorite lens.