The AI definitely follows the same ship-cap-scale as you, but bear in mind that it doesn't apply to starships (on your side or the AI's) so a Raid Starship is the same on Ultra-Low as it is on High.
Also, the total unit count it sends at you doesn't actually tell you much about the strength of the individual units. For some types of attacks it's actually handed a strength-budget and "don't make more than a few hundred ships for this", so if the strength budget gets much higher it doesn't send more ships, it just sends more powerful ships.
If you'd like you can see some fairly detailed math on what it gets for each attack and how the strength numbers add up.
1) Are these waves? Or exos (exo-galactic strikeforces)? Or CPAs (cross-planet-attacks)? Or something else? That determines what log file you'll care about.
2) Go into Settings, then the Advanced tab, then turn on "Enable Advanced Logging".
3) Run one of your "insane 10/10 cage match" games on high caps until the AI throws a few really major attacks at you.
4) Save the game, quit the application.
5) In your AIW directory's RuntimeData subdirectory (most common path is "C:\Program Files (x86)\Steam\steamapps\common\AI War Fleet Command\RuntimeData\") grab all the files that start with "LogicLog_" and stuff those in a zip file called "HighCapLogs".
6) Delete the LogicLog_ files from RuntimeData (now that you have copies in that zip file)
7) Run another 10-10-cage-match, this time on ultra-low caps until the AI throws a few really major attacks at you.
8 ) Save the game, quit the application.
9) Back in RuntimeData, zip up your LogicLog_ files into a zip file called "UltraLowCapLogs"
10) Come back here and upload both zip files (while writing a post, you can click the "+ Additional Options" below the big textbox, then click "Choose File" to pick something to upload) and I can point out the relevant bits of the logs to you