Tiling manager remove the need to resize. You use virtual desktop to switch between apps. If you need several apps side by side, tiling comes in place.

Tiling manager are often keyboard driven. If you use mainly your mouse/touchpad, it can be quite painful.

My feeling in floating window manager is that i soon as a window is hiding another, the one on top should just use all the available space, there's no point in seeing the one bellow. If you need information from 2 windows, it's much better side by side.

You might like the minimal tiling present in CWM (and likely other window managers, too). Basically, it is a regular old overlapping window manager but with keyboard commands as the primary control. If you have two or more windows you want to see on the screen at the same time tiling style, simply press the hotkey for either vertical or horizontal (Super+v for me). When I want to open a terminal window on top of a browser, pressing Super+enter puts it at the mouse cursor, scaled to the application’s default size.

For many terminal windows or one Emacs and one terminal, I might use tiling, but I can still overlap whenever it makes more sense. Plus, the consistent keyboard controls (I use a config pretty similar to https://www.c0ffee.net/blog/openbsd-on-a-laptop/#cwm) make me more efficient than a mouse interface.

Funny enough that's precisely my use case for tiling window managers. I'm often referencing one app to do work in another, and often one is just a bit too overlapped to see what I need, and I also need to lay windows out every time I do this work. With a tiling window manager, you can be sure that your app is not obfuscated, and there are various adjustments you can make to pane size and layout to get the right amount of screen space and positioning for apps. You can also save and restore layouts for particulars workflows.

I think the key difference here is the use of multiple virtual desktops in the tiling case. In my setup I typically have one vdesk for browsing, one for docs, one split between code/terminal. I may have others open for chat and music, and I can switch between any with one key combination, or resize with another. I love that when I open a new window it will maximize the screen real estate of wherever I put it.

Granted, I've been using i3 for more than half a decade, but I do agree with sibling posters on how 'freeing' the experience is once you get used to it. There is no doubt a learning curve; but in my experience it's on the order of days.