Every DAC Contour supports keeps its parametric EQ inside the DAC itself. Contour writes it from an Android phone: plug the dongle in, pick a profile, hold HOLD TO SEND. The dongle stores it.
Then the phone is out of the picture. The EQ works with every app, and on the DACs where Contour has confirmed it stays after unplugging, with every device you plug the dongle into: another phone, a laptop, an iPhone. No system equaliser, no app running in the background. Contour itself does not process audio; it only talks to the DAC.
EQ app on the phone
A phone EQ app changes the sound on that phone only. Plug the dongle into a laptop, and the EQ stays behind on the phone.
Wavelet calls itself a system-wide equalizer that works across many audio sources, not just one app. It has more than 5000 AutoEq profiles and imports profiles from autoeq.app or squig.link. It works with wired, Bluetooth and USB headphones and DACs.
Poweramp Equalizer works with most other player and streaming apps; in some cases the player's own equalizer setting has to be on. It has 5 to 32 bands and a parametric mode. The Poweramp music player is a separate app with its own EQ for what it plays.
USB Audio Player PRO plays through its own USB audio driver, bypassing Android's audio system, and its equalizer is part of the player. The app itself warns that it is not a generic system-wide driver; an optional Feature Pack can route other apps' audio through it on Android 10 and newer.
When the phone app is the better choice
Your dongle has no EQ inside, or Contour does not support it. Contour connects only to the ten DACs on the devices page.
You listen on Bluetooth headphones. An EQ in the dongle plays only through the dongle.
You want more bands than your dongle has. The DACs Contour supports have 5 to 10 bands; Poweramp Equalizer goes up to 32.
You want what an app adds on top of the EQ: Wavelet, for example, adjusts loudness to your volume and loads the right profile when you switch headphones.
You play everything in one player, such as UAPP, and only need the EQ there.
When the dongle is the better choice
You use the dongle with more than one device: two phones, a phone and a laptop, an iPhone.
You want the same EQ in every app, without checking which apps a phone EQ app reaches.
You want nothing running in the background on the phone.
You want the EQ to come along when you change phones.
Limits of an EQ in the dongle
It has the dongle's limits: the number of bands, the filter types and the gain range. They are listed for every DAC under Limits and troubleshooting.
FiiO says the KA15's EQ works with PCM up to 384 kHz/32-bit and not with DSD, and the K13 R2R's PEQ with PCM up to 192 kHz/24-bit.
The Kiwi Ears Allegro Mini tunes its filters for a 48 kHz stream, so a player that forces 44.1 kHz shifts every band about 8% down.
Changing the EQ takes an Android phone with Contour, or the maker's own tool. Playing it takes nothing.
Questions
Does the EQ in the dongle work on an iPhone or a PC?
Yes, on the DACs where Contour has confirmed the EQ stays after unplugging: it is stored in the dongle, so it plays on every device you plug the dongle into. Each DAC's page says what was confirmed. You need an Android phone only to change it with Contour.