In your specific examples, there is neither a difference in style nor in what the sentences express. They are pretty much equivalent.
Changing word order in German can be used to put emphasis on certain parts of the sentence, but it doesn't necessarily need to (especially if the parts of the sentence being emphasized align perfectly with the general meaning). The emphasis is put on the part of the sentence that ends up closest (or, in most sentences, directly next) to the conjunction.
I'll try to explain this by changing your sentence to
Er versuchte es mehrfach, doch ihm gelang es nicht.
Here, the "ihm" is closest to the "doch", which could be expressing it was "his" problem (maybe someone else would have succeeded).
Er versuchte es mehrfach, doch es gelang ihm nicht.
Is pretty much neutral, the emphasis is on "es", which aligns with the overall meaning of the sentence. (If "es" would be kind of non-aligned with the general expression - maybe, because "es" was dead simple - it might be different, but here, without further context, it apparently is).
Er versuchte es mehrfach, doch gelang es ihm nicht.
Is pretty much the same - The emphasis (now on the predicate) is again aligned with the overall meaning of the sentence.
It might be worth mentioning that the emphasis is rather subtile and might not even be noticed by a large amount of native speakers - So it is maybe slightly beyond the scope of someone not using German as a first language (Here the rule of thumb is: If you have to think about it, disregard it - in favor of more fluent speech).