Hi Lizzie,
First of all let me explain that today there are three different network generations in use:
- GSM which is considered being a second generation (that's why it's sometimes called "2G") technology and supports an older data transmission mode called GPRS delivering only 57.6 KBit/s and a newer data transmission mode called EDGE giving up to 236 KBit/s.
- UMTS which in many countries is called 3G as it's a third generation technology and originally supported only data rates of 384 KBit/s but was speeded up by a technology called HSPA and now can deliver up to 84'000 KBit/s, but most HSPA networks won't deliver more than single-digit thousands of KBit/s.
- LTE which is the latest, fourth generation (4G) technology and supports data rates of 100'000 KBit/s and soon probably even more. Despite LTE sounds pretty amazing there are still some issues with this new technology. One of them is that the industry still couldn't agree upon a standard for voice calls, so LTE networks lack a very basic feature, namely voice calling. Therefore LTE phones sold today need to (automatically) switch back to 2G or 3G networks once a voice call comes in or is being placed, which is kind of botchy and may result in failing calls. So LTE is still pretty immature but it may still make sense using it already today where 3G networks are congested and operators can't increase capacity due to limited frequency spectrum. E.g. that's the case for AT&T or Sprint.
Please note that some operators (e.g. T-Mobile USA) market their 3G networks as "4G" because they can deliver data rates similar to those on LTE networks, despite 3G networks are not 4G from a technical point of view. If you want to make sure that a 4G network is really a fourth generation network, ask the network is actually based on UMTS/HSPA or LTE.
Now when you look for compatibility between phones and networks you have to check the supported frequencies for each of these three network generations. Usually all modern phones support GSM on American GSM frequencies (850 and 1900 MHz) as well as the GSM frequencies used in the rest of the world (900 and 1800 MHz). So in regards of 2G/GSM networks modern phones have global compatibility.
But when it comes to 3G/UMTS you need to check frequencies separately. So a phone that supports 2G/GSM on let's say 900 MHz does not necessarily support 3G/UMTS on 900 MHz.
The same applies for LTE: If a phone supports 3G on a certain frequency is does not necessarily also support LTE on the same frequency.
So you have to look very carefully at phones' specifications and distinguish between these three network standards.
The Galaxy Note with the designation "GT-N7000" and probably the one you call "international version" does support UMTS 850/900/1900/2100 but it does not support LTE at all.
The AT&T version (designated "SGH-i717") in contrast already supports LTE on "Band 4" (1700/2100 MHz) and "Band 17" (700 MHz) (both used in the Americas only) but in turn lacks UMTS support for 900 MHz.
Now the question is what's more important for to you: LTE for faster Internet at home in the Staates or UMTS 900 which is only used outside the Americas.
In Europe 3G/UMTS networks have been rolled out primarily on 2100 MHz over the last decade so you'll usually experience perfect coverage with a device supporting only this frequency. Deployment of UMTS to the 900 MHZ band started only 3-4 years ago and only in some countries, where it is primarily used to cover rural areas (because signals on lower frequencies have a higher range and so you need less cell towers on 900 MHz than if you use 2100 MHz). In Germany (where I know you've been travelling to) we don't have UMTS 900 at all. In the UK however O2 have rededicated parts of their 900 MHz frequencies which were formerly used for GSM to UMTS (for details read
WirelessMoves: UMTS 900 in London - A Tough Decision). Vodafone UK have also done so, while the other British operators can't as they don't own any 900 MHz frequencies. Btw Lebara UK, which you recently were interested in, don't run their own network but use Vodafone's.
So whether you need UMTS 900 support or not very much depends on which country you are travelling to, which network you intend to use and also if you are staying in rural or urban areas. The latter usually historically have very good UMTS 2100 coverage while UMTS 900 just adds capacity to the existing UMTS 2100 networks there and closes some minor coverage gaps. In the countryside however lacking UMTS 900 support may result in your phone falling back to slow 2G networks since covering rural areas with a dense grid of UMTS 2100 cell towers often doesn't pay off due to the low number of potential customers. Such regions often get first-time 3G coverage only through UMTS 900.
After all this complicated technical explanations I would recommend AT&T's version with LTE-support since the benefits from being able to access AT&T's LTE network in the Staates should outweigh the rare occassions where UMTS 900 would provide better coverage or higher bandwidth while travelling in Europe.
I hope this answers your question.