What is the difference between cell phones from Nokia with "i" and without it at the end of the model number?
The i is basically a redesign of an older model. The 5120i added text messaging. Ditto with the 5185i (and 80i) The 6340i added the GSM 850 band.
That brings up something I've wondered about... why did the 5165 get a new number instead of just being labeld the "5160i"? There really isn't that much difference between the two. The 8265 I can understand getting a whole new model number as the form factor is slightly different some accessories aren't compatible, but the 5160 and 5165 are physically identical (faceplates are different but interchangable). Strange.
The 6590i would be your best bet as it includes the soon to be popular GSM 800 mode. This will elevate the chances of using your phone in more places in the future.