I'm not sure what you mean by private search shortcuts. Would this be a search box that you type something, press ENTER, and it does a search in a normal tab or I could do something else to make it search in a private tab? Or something as easy as Chrome's three dots > "New Incognito Tab" and I could immediately search from the URL bar would be fine.
Having played around with Firefox on my iPad, here are some things which are annoying (I mentioned a few of these elsewhere in this thread). I can see that many of these decisions were likely taking into account the limited real estate on an iPhone where I can understand the limitations, but it makes for a poor iPad experience. Safari and Chrome generally get these correct in a single app by adjusting the functionality based on the screen size.
- Adding a tab takes two steps: click the number box then
click "+" to add a tab.
- Closing a tab takes two steps as well. Why no "x" to close?
The "star" icon is exactly where I'd expect the close option
to be. Consider the frequency of someone closing a tab vs.
marking a URL as a favorite and the resulting UI should be
obvious.
- Adding a private tab is three steps: click the number box,
then click the Private Browsing icon, then click "+".
- Swapping between regular and private tabs involves three
steps: click the number box, enable/disable the private
icon, then click on the tab you want to focus on. In Chrome,
this is one step: click the Incognito icon which immediately
swaps between the most recent active tabs in each mode.
- You can only view one tab at a time. Not only does this make
switching between tabs tedious but you also lose context;
not seeing a tab you've opened in the background that you
mean to read later will generally go unread.
- "Settings" available via the tab management interface. This is
a rather unintuitive location to manage application settings.
Why not have app settings available from within the iOS
Settings app?
- Editing the URL of a tab hides the tab's content. Not sure what
the thinking was here, but if I want to access thumbnails,
bookmarks, etc. I'll do this from a new tab, not by manually
editing a URL. Consider the use case of a URL shown in a web page
but it contains tracking info. I might want to manually type it
instead of clicking, so when the page contents vanish it's
difficult to do that.
- Unable to search for text on the page.