jim,
i returned from a trip this past Sept and bought Pay As You Go (PAYG) SIMs from 5 different countries.
i should note that i have a Note 3 5.7 that i purchased outright late last year for my travels. Also, i can only attest to what i used and purchased. Since i only purchased SIM cards from vendors that had them (some were out!) and spoke english.
From what i can tell externally (as in operator interface and files) i have not noticed any changes. Internally, who knows, but i still have all of my contacts and such where i want/need/placed them. The SIM may add a desktop icon/link to their web site, but i just look at them and will dump them if they aren't important.
Just an important note. If you decide to buy a SIM overthere, make sure you can add minutes to it if you will be "roaming" around. Roaming will chew up your minutes faster. If you buy one in Germany chances are you will have to buy a "voucher" to add minutes. You can add more minutes when you buy the SIM too, but once you are out of the country of origin, you won't be able to buy a voucher, but you can add minutes via a voucher anywhere. I bought my vouchers at a gas station/convenience type store or at one of the provider shops around town. You need to know what provider you have too, but that shouldn't be an issue. You will need to buy the vouchers in certain denominations, but that shouldn't be an issue.
one other important issue.
Locked or unlocked phone. Samsung has installed "regional" locks in their new devices. You can google up on this and get educated. Being "low tech", is okay, but you should be an "informed" user. You really need to get your phones "unlock" code. If you have purchased your phone outright you need to get your code -period. Don't take any shop employees word that its "unlocked" since you paid for it outright. I did and my phone was locked. I found out when i was over in Europe trying to get my SIM to work. If you are from the USA, your phone will (should) work with any USA SIM. As soon as you install any non USA SIM it will lock if you dont have the unlock code. You can put your original SIM back in and it will unlock (for that SIM) and you can use it again, but only for that SIM.
Before you go, jot down the providers 1-800 or whatever number for help/assistance. IF you're lucky, they may have a world 1-800 number to call. Also, just an fyi, from what the service people told me, the unlock code can take anywhere from 24 hours to 1 month to get from the manfuacturer. If they dont have it, they cant give it to you. The manufacturer has to pass on that info, and from what i can guess, that info maybe lagging.
good luck and happy trails.