I have had three BMW motorcycles, and everyone of them had recalls, and issues. My K1200R Sport is rock solid. I have had mine for about 6 months and have only put 3 thousand miles on the clock because I also have an RT. What I paid for the bike was so obscenely low that I am not even going to mention it.
It is extremely versatile. But, like every BMW motorcycle, standard maintenance is expensive through BMW. I wouldn't be concerned about buying one. Most of the time, what you hear on these forums is bad because people have issues (with every bike), and they like to complain. People are not always vocal about good as much as they are about bad.
Differences between the two?
The K1300r is more refined then the 1200. It has better fuel mapping.
The initial 1200r had surging and idle irregularities. That was corrected past '06 and recalls.
The K1300r clutch configuration has been updated (it also can be ordered with shift assist).
The early K1200r had assisted brakes (wizzy brakes). The 07 changed that.
The k1300r has been tuned for a little better performance and claims a little more HP
The K1300r has no more fuel strip to go bad. The K1200, like all the other BMW bikes (prior to '09) all use electronic fuel strip to operate your fuel gauge, distance to empty, etc. Those are prone to failure. My RT has gone through 5.
Both Bikes are great, but the 1300 is not offered in the USA at all. So if you are here in the states, there is no R bike. You would have to go with a S1000r or an S1000XR.
That is about all I can think of at this point. But, so you know, I love my K1200r sport.