On looks? Muddies look cheap and clumsy compared to Muckboots, that may just be dreadful advertising shots though.
Choice of colour is limited to green, prices seem to be quite cheap.
Muckboots come in an ever increasing range of colours and designs, more expensive than Muddies.
Personally? I've never come across Muddies so cannot comment about comfort or performance.
I have had Muckboots of various designs for years and have worn them until they disintegrate. I can only speak as I find, my Tynes are great, warm enough in winter that I can just wear thin socks, comfortable and I have never found them slippery in icy conditions which is a complaint I have often read.
Just to add to your confusion, there are Just Togs Mudruckers too! http://www.justtogs.co.uk/footwear-mudruckers.php
My local tack shop said they wouldn't sell Muck Boots again because they had so many split ones back, but they hadn't had any Mudruckers back at all! They also do a version with a sole suitable for riding in - bonus!
I'm wondering if muckboots have gone out of business? I couldn't get through to them on the phone and all emails bounce back, supply problems have been terrible and the wholesaler has stopped dealing with them and are promoting a brand called Rok instead.
That's interesting. Both my daughter and myself had a pair of muckboots which didn't last very long. After only a couple of months there was a split in the back of the heel. I bought a pair of Muddies when I went on a riding holiday in Iceland and they were brilliant. Two years on and I'm still using them.