OmniFocus for iPad has improved a lot to the point I don't feel I'm missing too many features from the Mac version (though there are still some awkward parts in the UI, e.g. moving/creating folders and projects) and even has support for Omni Automation Plugins now, in addition to Shortcuts support.
Web version sadly has no persistent offline storage as you said. It's also veeerrrrryyy slow since every click requires a roundtrip to a server that made slightly acceptable thanks to WebSockets (I don't live in the U.S. where their servers seems to be located). I'm connected most of the time so offline storage is not that much of a concern for me. I wish Omni Group put more effort into it though, given they charge $50 a year on top of a standalone app, which is way more expensive than Todoist. :(
Web version sadly has no persistent offline storage as you said. It's also veeerrrrryyy slow since every click requires a roundtrip to a server that made slightly acceptable thanks to WebSockets (I don't live in the U.S. where their servers seems to be located). I'm connected most of the time so offline storage is not that much of a concern for me. I wish Omni Group put more effort into it though, given they charge $50 a year on top of a standalone app, which is way more expensive than Todoist. :(