In general, it will use LTE/HSPA+ in compatible regions, and drop to 3G in the rest. So you'd basically want to select based on where you're using 4G-like services the most.
Other things to consider are which 3G bands the phone supports: you might find it doesn't support 3G worldwide.
Also, if the phone is locked and you use one sim card worldwide, you might choose an LTE model but have a sim card from a provider in a non-LTE market, and find the phone won't automagically roam onto LTE because the LTE provider in the US isn't a roaming partner.
With questions like this, just giving the exact model of the phone would have had someone give you a definitive answer by now, if only by pointing you to the right specs page on the website. Anyway, it sounds like an S3, in which case the US version MAY have a less powerful CPU than the international version; I've not looked at the most recent specs. I presume the HSPA+ version would roam onto T-mobile in the US.