I have used 4-teat (2 front 1 each side) and 6 teat (3 a side, sits on a hurdle) and the 4 bottle rack system.
Sits-on-a-hurdle is hard to make robust, yes, it's easily tipped. But since you'll be there you can steady it by hand, so it's not too much of a problem, I think.
4-teat works well, although this one had harder plastic teats and some lambs become so greedy they start to make their mouths bleed when they drink!
Downside with buckets is that you can't see exactly how much each lamb is getting. You have to sort them into batches that drink about the same speed and need about the same amount, and/or pull them off as their tummies reach the requisite roundness. Another slight downside is none of the systems I have used completely drain the bucket, and I am rather particular about only reheating milk once, so then I either discard some milk each feed or have somehow to use the dregs up in a way that ensures it doesn't get mixed into the next bucket-load and end up in the dregs-to-be-reheated again.
Upside with buckets is it's really quick and easy.
My preference, however, is the bottle rack. You know exactly how much each lamb is getting - and if the 4 drink at roughly the same speed you don't get bottle-swapping while there is still much in someone else's to steal! It's a little bit more effort to use, as you make up a bottle per lamb and put each bottle into the rack one by one.
If I had several multiples of 4 lambs I might go on to the bucket, but at present I have 4 on the rack and I feed the other two with bottles by hand at the same time, so that works well.
I have never used a Shepherdess myself, partly as I enjoy the interaction with the pet lambs and so do all our visitors and partly because I was put off by the idea of milk being kept warm for long periods - or feeding unwarmed milk. I prefer the lambs to be getting either freshly-made milk or reheated-once-only milk. But again, if I had the numbers I am sure I would reconsider my position!