There are many common points there (per instance, does Gaia equal Lorien - preservation and harmony of nature etc etc?). But they seem to differ in one of their main points, though, namely, freedom of Men (or individual man, to be more precise) (I deliberatly do not mention Eru/lack of corresponding being with Asimov, since it's obvious):
In Tolkien, humans progress from 'watched/guided/protected' mode to independent
Dominion of Men, and are 'free to shape their life...' etc. In Asimov, the process is reversed - humans start off as individual free agents, the transitions being Foundation - seemingly independent society, but its actions are
Mene Takel Fares, and Gaia - common Intellect, something like mental anthill, with the higher mode of existence seen as future union of the whole Galaxy (and probably whole universe further on) into one 'Consciousness', with the idea that process is part of necessary progress, part of the road to survival, and should be undergone despite of incontestable unwill of many individual humans to be so united. Besides, Robot/Valar parallel may be drawn, but robots are: A. Man's own creation B. Become Valar-like entity (i.e. Power behind the events in the Galaxy/protector/conductor of Fate) only by the end of the series. Idea is plausible - to the great extent, Valar are servants themselves, but not in the mode Asimov developed his robots.
I very much like idea of Fate being rendered and calculated mathematically, though
. Imagine Mandos doing equations, typing feverishly on his 'Fortunium IV ('Valintel Inside)' PC's keyboard? And all those elves thinking he is being prophesying...