I recently decided to get back into birds and wildlife (been shooting mostly people and landscape), and I ended up spending 4 months trying lenses and deciding. I set my budget for my long lens at ~$1000, as it is not one I'll be using for paid work. This ruled out obvious contenders like the 100-400 mk II, or any of the bigger, faster telephoto primes. Left on the short list of lenses that could be used for my purposes and fit the budget were these:
Canon 300mm f/4L IS + 1.4x II/III*
Canon 400mm f/5.6L**
Canon 70-300mm f/4-5.6L*
Canon 100-400mm f/4.5-5.6L mk I**
Sigma 150-600mm f/5.0-6.3 C**
Tamron 150-600mm f/5.0-6.3
The 3 in bold are the lenses I ultimately narrowed things down to
*Lenses I've owned in the past and used extensively
**Lenses I rented or borrowed over the past year and used only once or twice
I ruled out the Canon 300/4 based on my prior experience; it was an average performer on the 5DSr, not really up to today's sharpness standards for primes, and with the downside of having to swap the 1.4x extender on and off to zoom. Its IS was also behind the times, compared to newer lenses I've owned like the 70-300L and 100L macro.
I ruled out the 400/5.6 for the lack of IS. I know from experience with the 70-300mm and 300mm f/4 IS that IS is super useful for relatively still critters. I didn't want to have to use higher ISO in order to get hand-holdable shutter speeds with still or slow-moving subjects, the relative slowness of an f/5.6 lens already has me shooting higher ISOs than I like when it's not bright daylight. Because long-distance bird shots are often heavy crops, I care about noise more than I normally would in a landscape or people shot.
I rented the 100-400 mk I. This was the easiest of the bunch for me to rule out. Image quality was noticeably inferior to my 70-300L and Sigma, and the lens is bulky and has that pump action I wasn't personally loving. I know this has been a much-loved birding lens for years, but I didn't find that it performed to the standards set by the newer lenses I tested. Bear in mind this was also rental gear, and I didn't take the time to MFA it (due to knowing right away the pump-action was not for me), so not a 100% fair evaluation.
This left me considering re-purchasing the 70-300L lens I sold a year ago to fund my 85L II purchase, or to try one of the new third-party 150-600 lenses. The L was again a strong contender: compact, sharp, weatherproof. I can't say for certain that I won't end up owning again also. But in the end, I was wooed by the allure of 600mm of reach, and the realization after reading/watching reviews and trying the Sigma that these third parties have really upped their game as of late. The Sigma and Tamron both looked fine, and I chose the Sigma based on the appeal of the USB dock for user updates, and various reviewers I trust giving it a slight edge in terms of IQ at the long end (especially the corners).
There is an obvious downside to the 150-600mm offerings, as compared to the lenses in the title of this thread: their weight. At 1930g and 1950g, the Sigma and Tamron are ~55% heavier than the 400/5.6L and ~40% heavier than the 100-400 mk I. They are nearly double the weight and length of the 70-300L!
So, for now I've got the Sigma 150-600mm Contemporary lens and I'm using it on weekends around the bay area. The image quality is noticeably better than that of the 100-400mm mkI I rented, though not up to the performance of the mk II. The next time I go on a long distance trip though, I will certainly be thinking again about the Canon 70-300L, for its more travel and carry-friendly size.