Battery: the short answer
Dictation only uses power while it is running, and it runs for a few seconds at a time.
That is the detail that makes the whole question smaller than it looks. Speech recognition is not a background service listening all day. The microphone opens when you press the key and closes when you finish, the model does its work in a burst, and then nothing is happening at all until the next time you speak.
For most people that adds up to a few minutes of processing across an entire day, spread over dozens of short bursts. Compared with a few minutes of video, a navigation session or a video call, it is not the thing draining your phone.
The comparison nobody makes
Cloud dictation is often assumed to be lighter because your phone is not doing the recognition. That skips what it is doing instead.
Sending audio means keeping the radio active, and the radio is one of the hungriest components in a phone, particularly on a weak signal where it has to work harder to hold a connection. Recording, compressing, uploading and waiting for a response is not free either.
So the honest framing is not "local costs battery and cloud does not". It is that one approach spends power on the processor and the other spends it on the network, and which comes out ahead depends on your signal quality more than anything else. In a fringe reception area, local is usually the cheaper of the two.
What genuinely does affect battery
Three things, in order of how much they matter.
How much you dictate. Obvious, but it dominates everything else. Someone dictating a hundred messages a day is doing far more work than someone dictating five.
Which model you chose. A larger model does more arithmetic per sentence, so it costs more per dictation as well as taking longer. On a phone where battery matters more than the last few per cent of accuracy, the smaller option is the sensible choice.
How old the phone is. Older processors take longer to do the same work, and the burst therefore lasts longer. This is the same reason a smaller model helps disproportionately on older hardware.
What does not matter much: having the keyboard installed. Typing is not expensive, and when you are not dictating, no speech model is loaded or running.
Storage: the number
This is where local recognition has a real, unavoidable cost.
The model has to be on the device. LocalType offers three: 60 MB, 190 MB and 539 MB. The middle one is the default recommendation and suits most phones.
Only one is kept at a time. Downloading a different size replaces the one you have; it does not add to it, so experimenting does not slowly consume your storage. During installation you briefly need room for two copies. Keep that in mind if your phone is nearly full.
Set against the storage a few dozen photos occupy, that is modest. Set against a phone with 3 GB free and a warning light, it is a real decision, and the 60 MB option exists precisely for that case.
Memory, which matters more than storage on old phones
Storage is where the model sits. Memory is what it needs while running, and that is the constraint people actually hit.
A model has to be held in memory to do its work. On a phone with plenty, this is invisible. On a phone that is already juggling a browser, a messaging app and a few background services, a large model means the system has to evict something else first, and that shows up as a pause before your text appears.
The practical rule: if dictation feels slow, try a smaller model before concluding the phone is too old. On the test handset, one with 4 GB of memory, the middle model turned 6.9 seconds of speech into text in 4.1 seconds, while the largest takes roughly twice as long as you spent speaking. On a device with less to spare, that gap widens considerably.
Data, which local dictation removes entirely
This one counts precisely because nobody counts it.
Audio is much larger than text. Cloud dictation uploads it every time, which on a metered plan or while roaming is a slow trickle of charges for something that did not need to leave the phone.
On-device recognition sends nothing at all. Your allowance is untouched by dictation whatever you use it for, and the only network activity in the whole product is fetching the model you chose, once.
What else lives on the device, and what does not
The complete list of what the app keeps on your phone is shorter than people expect.
The model file is the large part. Everything else is small: your settings, and the words you added yourself, which stay on the handset and are given to the speech model as context so your names come out right. Those additions are also what makes the app's dictionary useful across all eighteen languages it covers.
What is not stored is the audio. No archive of your recordings is kept, because the sound becomes text and is finished with. So dictation never creeps up on your storage over the months, the way a voice recorder would.
The app's data is also deliberately excluded from Android's cloud backup. That has a practical consequence on a new phone, where you install and download a model again instead of having it restored, and a storage consequence on your current one, where nothing at all is being duplicated anywhere else.
There is no advertising in the product and nothing inside it tracking what you do, both of which would otherwise be background activity costing a little battery of their own. In password fields the microphone does not appear at all.
What to do on an older phone
Four adjustments, roughly in order of effect.
Pick the 60 MB model and leave the default alone. It is noticeably faster on limited hardware and the accuracy difference is smaller than the numbers suggest for clear speech in a quiet room.
Close what you are not using before a long dictation session, since memory pressure is the main cause of slowness.
Dictate in sentences rather than paragraphs. Shorter bursts finish sooner and sit in memory for less time.
And check free storage before downloading, remembering the temporary need for room for two copies during installation.
Battery, storage, memory, data
Battery: a few minutes of processing spread across a day, less than most people assume, and not obviously worse than the radio activity cloud dictation requires.
Storage: between 60 and 539 MB depending on which model you pick, one at a time, each new one replacing the last.
Memory: the real constraint on older phones, and the reason to reach for a smaller model instead of a newer handset.
Data: nothing, ever, which is the one line in this comparison where local wins outright.