If China pays more attention to Burma than the US does I suspect it is for the foillowing reasons:
1. Competition with India for commercial goods export to Burma;
2. Competition with Russia and India for weapons export to Burma; (I believe Burma has one of the 20 biggest armed forces in the world.)
3. Access to Burma's natural gas reserves (only 21.1 TCF according to EIA, but still worth exploiting due to proximity--by way of comparison Venezuela has 181 TCF of known NG reserves and the US has 211 TCF according to EIA)
I don't think a "basing for terrorism problem," a la Pakistan-Afghanistan, is a significant concern for the Chinese vis-a-vis Burma. The military junta seems to have a pretty firm handle on dissidence (and what it doesn't control, the opium drug lords in the Golden Triangle do I suspect). I'd be more worried about the Burmese getting sucked into a Chinese sphere of influence, thereby making the Indians worried. This could produce new tensions on the eastern side of the sub-continent to go along with those that are already in place on the western side.
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