As already mentioned by @EarnestAl, the suites are based on different principles.
As long as the documents (text, spreadsheet, presentation) are quite simple, you should have a fairly good acceptance in LO. But if they are sophisticated, expect difficulties.
The right answer depends on what you do with your documents.
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If they are private to you (not sent to external recipients)
When you need them, translate them into native features so that the documents end up in “pure” ODF.
Expect a lot of manual work:
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Writer will “import” .doc(x) and make approximate conversions; the global structure will be messed up and it is very difficult, perhaps impossible, to fix the structure.
The cleanest way I found was to copy DOC(X) contents and paste as unformatted text. This means all formatting is lost but you don’t import Word idiosyncrasies.
Then you reformat the document. Forget your Word muscle memory. The right way to do it is with styles. Styles are much more developed in LO than in Word. In particular, you have character, page, frame and list styles, of which Word is totally unaware and manages as direct (manual) formatting.
Before undertaking conversion, you should read the Writer Guide and practice a bit on example one-shot files. Then design your own styles. Note that direct formatting in Writer is the cause of many formatting “surprises”. Contrary to common belief, direct formatting is not intuitive nor simple. Succeeding to format a document with direct formatting need guru level to understand all its subtleties.
- Function names in Calc may be different and the arguments too.
Note that any VBA macro will not work because LO uses a different language (a variant of Basic or if you prefer Python).
Here too, you can use styles (and this is also recommended).
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If you share your documents in a collaborative environment
It is preferable to use the same application. As already mentioned, editing sessions in different apps has a cumulative effect leading to quick unrecoverable damage due to iterated conversions between format. Usually, this ends up in encoding the least-capable features and losing formatting or presenting weird appearance.
In summary, the suites are fairly compatible for quick’n’dirty display of file contents. Adoption of one or the other is a matter of workflow. But if you opt for LO, the best thing is to restructure the documents the LO way.