@oristarA,
I would say tilt and inclination basically mean the same thing in this context. But in the context you cited, I might also read a element of implied shift, or change.
One can be inclined and/or one can become inclined (or more inclined than he was). I don't know the facts, but I would be led to assume (without concluding for certain) that this particular budget was "more" inclined toward R&D than the prior one.
If you "tilt" something (like a glass of beer), there is often an element of "action" and change involved. But it can be used as either a verb or a noun (a static orientation), as far as I know.
As far as the "use" element of your question goes, yeah. Practical use or practical "allocation." But it could mean something else, I suppose. Obama might have, for example, allocated more to one item than another for "practical" reasons of a different nature (such as getting more votes). But I don't see that as being suggested here.
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