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It's not that one is better than the other - they are just different and which is better depends on circumstances.
In general, if you want a small decrease in expected time to completion, then use fast tracking (doing tasks in parallel which are normally done in series). A little bit of overlapping, if handled carefully, does not usually involve much risk. Extensive fast tracking can result in serious delays if things go wrong.
For a big decrease in time to completion, you normally need to use crashing (adding additional resources). This is expensive and has its own risks. If your new resource is people, they will have to be brought up to speed on the project which of course takes time.
Neither of these techniques will be effective unless they are applied to the critical pathways of the project.
Fast tracking and crashing are two schedule compression techniques that help you shorten the duration of your project.
Fast tracking does not involve any cost but it increases risks. On the other hand, crashing does not introduce much risk but it is a costly affair.
With crashing it is also possible that you will not yield an effective work output because you may not get skilled resources, and even if you get them, it takes some time for them to settle down. You cannot bring a bunch of people together and expect them to perform immediately.
Therefore, perform due diligence before going for crashing, because sometimes it may increase the cost significantly with a poor reduction in schedule compression.
