M4A is what an iPhone voice memo, an Apple Music download and most modern podcast apps produce, and it is technically the better format. The reason to convert is almost never quality — it is a device or a piece of software that only understands MP3: a car head unit from before 2010, a gym treadmill's USB port, a DJ or transcription tool with a fixed importer, or an upload form that rejects the extension outright. Because both formats are lossy, this conversion re-encodes rather than repackages, so it is worth doing once from the best copy you have rather than repeatedly.
The .m4a extension does not tell you what is inside
M4A is a container, not a codec. The same extension is used for AAC, which is lossy and what iTunes purchases, Apple Music downloads and iPhone recordings all use, and for ALAC, Apple Lossless, which is a bit-exact copy of a CD and is typically five to ten times larger. Both open in the same apps and both show as “M4A” in a file listing.
The conversion handles either without you having to know which you have, because it decodes to raw audio before re-encoding. What differs is the outcome. Converting ALAC to MP3 discards real information you had — keep the original if it is your only lossless copy. Converting AAC to MP3 is a second lossy pass over audio that has already been through one.
Why the MP3 can be larger than the M4A it came from
AAC is a later design than MP3 and simply encodes more efficiently: a 128 kbps AAC file is generally held to sound like a 160–192 kbps MP3. To avoid making an audible downgrade the conversion encodes at a high variable bitrate rather than matching the source number, so a 4 MB M4A frequently comes out as a 5 MB MP3 that sounds slightly worse. That is not a bug in the conversion; it is the cost of the older codec.
This is also why converting back and forth is worth avoiding. Each lossy re-encode works from the previous encoder's output, not the original recording, and the artefacts accumulate. If you need both formats, convert once from the M4A each time rather than chaining conversions.