Multiple Wi-Fi APs: Use same or different SSID?

I have multiple Wi-Fi access points in my house. What's the best practice, should I use the same or different SSIDs?

I currently have different SSIDs because I like to know which AP I'm logged in to. But handover takes ages. Would that work better/faster when using just a single SSID?

My clients are mostly iPhones and iPads and the APs are non-Apple (AVM Fritz!Box and Digitus).

You can have the same SSID for multiple APs, this is how our campus network is set up, but there is a caveat that's worth knowing. When moving between APs we've noticed OS X has a tendency to "stick" to the first AP it has joined even if it's in the presence of another AP offering a stronger signal. Cycling the wi-fi can help with re-association to an AP with a stronger signal, but the fact is it doesn't always switchover automatically. Unlike Windows which allows you to tune the aggressiveness with which it searches for better APs, OS X offers no easy control over its wireless behaviour.

This may seem like a non-answer but you may find you have as many issues (albeit slightly different) with a single SSID when compared to a network with multiple SSIDs.

My advice would be to try it for yourself and see how it works for you. Be prepared for some experimentation with setting wireless power levels on your APs so you can have some overlap between APs, but not so much that OS X will doggedly stick to the first one it finds.

I've changed the setup to use the same SSID for all APs and I observe much faster handover times, at least on my iOS devices. Haven't done yet any tests with Macs though.

So far I haven't reduced power levels as @ScunnerDarkly suggested because I'm satisfied with the results right now.

It seems like you are pretty up on WiFi, so I won't go into all the inner workings. However, you did mention that the "handover takes ages."

The handover is handled by both the device AND a controller. There is a setting (and generally not accessible by users) at what threshold the adapter begins looking for another good network. It is taking ages because it takes that long for the signal to drop off. Once it does, your device connects to next available, strongest network.

Simply speaking, the controller helps with this process by monitoring signal strength of the connected device and then kicking off the low ones to force a rejoin.

Since those controllers cost mega $$$, it is much easier to just toggle Wi-Fi on/off. Setting your AP SSID is now just a matter of preference.