Both are horribly slow, seriously, try iTerm2 for a week then try Terminal - you'll then notice how much latency iTerm2 adds to basic key presses.
oh-my-zsh is also horribly slow out of box, spend some time manually configuring zsh and observe your terminals open in fractional seconds instead of multiple seconds.
iTerm2 with the new metal renderer (only added to the stable releases recently) is as fast as Terminal. But if you want to see what a truly fast terminal can be, give Kitty a try: https://sw.kovidgoyal.net/kitty/
As for OMZ, yep, it includes a lot of functionality out of the box which makes it a little slow. I personally use prezto because it's quicker. Give that a try.
I don’t know about color (never needed anything fancy that way) but Terminal has supported ligatures for at least the past macOS release or two. I use Fira Code with mine and it works exactly as expected.
iTerm2 is nice but for my usage it does too much. If there were a lite version that cut a lot of the more niche features and focused solely on speed and responsiveness I might consider it.
I use iTerm2 all the term and I can honestly say I've never given a second thought to responsiveness. What are you noticing specifically? Are you typing super fast?
My terminals stay open inbetween computer re-boots, so not really a problem? I imagine most dev-types keep terminals open all the time on their local dev machines.
I know this is territory that gets rehashed every time someone says "hey, I like tool X..." but I still get a kick out of browsing these threads to see what tools people are using.
If you want one persistent window to always popup with a hotkey:
Preferences => Profiles => (Choose or make from scratch[1]) => Keys => Configure Hotkey Window
I think that works with the Control-Command-Space binding mentioned above. I use caps lock to toggle my terminal, which required some remapping via Karabiner[2]
[1] I have a profile called "Hotkey Profile" I don't remember if I set this up myself or if iTerm did it for me. I have it configured to appear on whichever monitor my mouse is on when I open it, and to have its window fill the bottom 1/3 or so of my screen
To each his own: I find Terminal.app to be one of the best terminal out there, all platforms combined. Speed and latency are awesome, colors are exact. Line marks (both manual and with automatic prompt detection) navigated with cmd+up/down is a godsend. Escape sequences to update tab and window titles with directory and document paths are great too. The only thing I miss is having different settings for alt and meta on the left and right alt keys. The days of Terminal.app being crap (up till Leopard) are long gone since Snow Leopard where it had a major update, and was constantly improved upon on each subsequent release.
oh-my-zsh is also horribly slow out of box, spend some time manually configuring zsh and observe your terminals open in fractional seconds instead of multiple seconds.