I'm in Canada, and I have a 64gb Xiaomi mi 5s.
Some notes about this phone: -The phone doesn't have a global ROM yet - I have the China rom (English+Chinese support only) on mine at the moment. It has several bloatware chinese apps (most can be removed), and doesn't have the play store by default. It's not hard to install Google play, and there are guides to do it, but it is an extra step, and there are a couple minor issues (for example, play store links open in the Mi App Store (chinese store), which is quite annoying - apparently can be fixed via root) -LTE doesn't work in North America. 4g works very well on my carrier (on Telus's network). I believe it should work with some of the major carriers in the US (AT&T and Sprint? Not 100% positive). Will also work (sans LTE) on the other "big" carriers in Canada (Rogers/Bell/Fido). -GPS is a big odd. Outside and near windows, it works great, but I suspect there are some issues with the assisted GPS, as it has trouble finding location solely by cell towers and wifi. I've done some reading on this, and believe it can be fixed, however, it would require root. Not a huge issue for me though. GPS works very well outside - gets a location lock very fast. -So far MIUI seems like a great ROM. Far better than TouchWiz or the other manufacturer's various ROMs. Although I'm not a fan of the default launcher - I replaced mine pretty quick.
Overall, it's a really good phone, but unless you don't mind a bit of extra work/oddities it may be better waiting for global ROM.
Regarding your other questions:
Are their other phones which would be better in your opinion for the same price?
Mi 5 (not Mi 5s) is another option. It's a little older, but still quite a good phone from my understanding. I have no personal experience with it though.
Im new to android, but I read that Xiaomi uses a own version of android which will make it slower and not update as frequently. Is this true?
They use MIUI, which is built on Android 6 as of now. It seems to be updated fairly often, but it will not be as up to date as the new Pixel phones. There are also a couple different options for MIUI - there are the China and Global versions, and each has a standard and developer build. China version only has Chinese and English support, some chinese apps installed by default, and no google play installed. The global version has more supported languages, google play installed by default and none of the Chinese apps installed by default. Currently the mi5s does not have a global version available.
And I also read something about CyanogenMod being released for Xiaomi phones. What does this mean for a user like me?
Cyanogen isn't released for all their phones. If it's available, it means you can install a ROM other than MIUI - it will be closer to stock android, and may be more up to date.
Could someone tell me their experience with Xiaomi?
I have the Mi5S 64gb in Canada. LTE does not work in North America, although normal 3g/4g works great on most major carriers (at least in Canada - should work on some of the big carriers in the US as well). It's a really good phone (hardware is top-notch), but unless you don't mind some extra work (installing google play) and some oddities related to the ROM, it may be better to wait for the global version to be released. That being said, you can also update MIUI to the global version when it's released if you get it now.
If you have any other questions I'll be happy to answer.