I'm not the best person to ask, and I don't fully understand segwit, but I think it's the Core devs (partial) solution to the problem of scaling up the network without increasing block size.

IIUC, segwit makes certain kinds of complicated transactions easier to handle (ones with lots of inputs/outputs), possibly allowing more transactions to fit in less space, and lays useful groundwork for overlay networks like Lightning. I think the thinking is that overlay networks can be fast, and eventualy reconcile against the slower bitcoin network.

Unlimited would rather just scale up the bitcoin network in place, instead of relying on an overlay network.

You'd probably get better information from bitcoincore.org and bitcoinunlimited.info, or the subreddits /r/bitcoin and /r/btc (for core and unlimited, respectively, they split after moderator shenanigans in /r/bitcoin).