As an APS-C mirrorless with a very small body design style, it actually sits pretty firmly between DSLR and M4:3...I've shot with DSLR and A6300 side by side for a few years, and there is a noticeable overall size and weight difference, even despite the same size lenses for long reach. While M4:3 bodies designed for wildlife shooting and AF speed tend to be quite a bit larger, approaching DSLR size themselves - the lenses due to the smaller sensor can indeed be lighter and smaller. And while APS-C DSLR and APS-C mirrorless would both need to share the same size lenses, and honestly most long lenses tend to be designed for full-frame for both of these types of mounts anyway, that doesn't mean that they can't design lighter lenses even for full frame, as evidenced by the Sony and Canon 100-400mm lenses which are quite lightweight compared to the same focal lengths years ago, or the new Sony 400mm F2.8 which is very light compared to other full-frame lenses in that range. M4:3 lenses will always have potential to be smaller and lighter - but as focal lengths get up to 400mm optically, no interchangeable system lens is 'light' - look at the Panny 100-400mm lens at 6.75" and over 2lbs...definitely smaller than Canon or Sony's version, but no one's putting it in a pocket.
As for being 'much slower than MFT on fps' - the top spec Olympus at 18fps with tracking does have a higher fps than the 11fps with tracking Sony bodies, though how important that is to a birder would be up to the individual. There are also caveats: That's the only M4:3 body that has OSPDAF focusing that can match APS-C and full frame PDAF tracking abilities, and to get 18fps you have to use the electronic shutter, which can't be used for fast moving subjects without suffering rolling shutter effect. With mechanical shutter, that camera is capable of 10fps with continuous autofocus, so pretty much a match for the Sony's 11fps. I have been birding for many years with many different camera bodies, both DSLR and mirrorless, and I honestly have never used the top fps drive mode exceeding 8fps...more than that to me just means I have too many photos to sort later. I find 5fps to 8fps to be a sweet spot - enough frames per second to catch crucial wing positions and eyes open, but not so much as to leave an overwhelming number of frames of the same bird to sort through later. If I had a camera capable of 20fps with tracking, I'd still be shooting it at 7-8fps mode.
Other factors to consider with APS-C sensors over M4:3 would be the higher overall resolution, with 24MP and larger pixels, there tends to be more room to crop and still retain good overall resolution for prints or high-def sharing...and the slightly better high ISO abilities, shooting in low light or dusk where you can shoot comfortably at ISO 6,400 and push even higher as needed, with better shadow recovery, and less noise reduction needed in post.
Rather than defend one line by insulting the other, better to just enjoy the options and accept that they're all pretty darn good systems. Choice is good - you've got big DSLRs with big sensors, big DSLRs with medium sensors, medium DSLRs with medium sensors, smaller DSLRs with medium sensors, medium mirrorless with medium sensors, small mirrorless with medium sensors, medium mirrorless with smaller sensors, and small mirrorless with smaller sensors - each level down, even with long lenses, saves a few inches here, a few ounces there. Every camera has some advantages, and some disadvantages. Each person finds the Goldilocks system for their needs.