The critical difference is that ~たら assumes that the prior action has been completed before the subsequent action begins. Accordingly, a more accurate translation of ~たら would arguably be ‘once’.

仕事しごとわったら有楽町ゆうらくちょうく。()
Once work has finished I’ll go to Yurakucho.

In other words, we can’t start going to Yurakucho whilst we’re still working. One action needs to finish before the other starts. とき, on the other hand, is more flexible in this respect, although for actions that are naturally sequential ~たら is usually the better choice.

仕事しごとわるときに、有楽町ゆうらくちょうく。()
When work has finished I’ll go to Yurakucho.

Note also that the tense of the first clause does depend on the relative timing of the action (as it does in English).

仕事しごとわったときに、有楽町ゆうらくちょうった。()
When work finished I went to Yurakucho.

For other sentences the difference is less distinct.

えきいたらあめっていた。()
Once I arrived at the station it was raining.
えきいたときに、あめっていた。()
When I arrived at the station it was raining.

Both sentences are acceptable here because we don’t know when it started to rain, anyway.

At other times the meaning changes substantially.

とうさんは新聞しんぶんんだら、ラジオをく。
Once my father has read the newspaper he will listen to music.
とうさんは新聞しんぶんむときに、ラジオをく。
When my father reads the newspaper he listens to music.
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