Wildlife Zoom Lens for Micro Four Thirds?

Hi,
Anyone have a recommendation for a wildlife zoom lens for the micro four thirds platform (shooting Panasonic GH5. I’m a beginner to intermediate level hobbyist)?

Purpose: primarily filming big game animals (would like to take decent pictures as well). Considering the habits of big game animals, as opposed to birds, I think I need the versatility of a zoom lens over the sharpness of a prime lens and something that’s decent in low light.

Budget: ~$2,000

Micro 4/3 native lens vs full frame?
My research has led me here: Should I get the Panasonic Leica 100-400mm f/4-6.3 (full frame equivalent of 800mm. Huge reach! I think a major benefit for big game)…

…or is there a better full frame lens, that I could use with a Speedbooster, that would serve my needs?

The Sigma 150-600mm f/5-6.3 seems popular:

Other lenses I should consider?

Thank you!
Dave

Hi Dave, This is Neil and I own Olympus professional cameras and shoot a lot of bird and wildlife photography. I own the Leica/Panasonic 100-400 f4-6.3. For the first two years of my bird and wildlife photography this is the only lens I used and then two years ago I purchased the Olympus 300mm f4. since I photograph mainly birds I have switched to using this lens more but I love both. I would give the quality of the Leica/Panasonic lens at 100 mm and 200 mm as A to A- quality. As you zoom out longer to 300 and 400 mm I would say it goes down to B+ quality if the subject is farther away and if pretty close A-. It is a high quality, weather proof lens. I usually carry both with me. the 300 mm is always A+

I would stay with micro four-thirds for ease of use and size since they are both very good lenses.

If you want to talk more you can send me your phone number and I can give you many more details.

Peace,

Neil

Thank you very much, Neil. That’s so helpful! The 100-400mm seemed like an excellent choice, but it’s so reassuring to hear it from someone personally before dropping all that money.
Best,
Dave