I did some comparisons on the stock DGTPi (Pi3b) between my PicoChess v3.3 Lite RPiOS image and one made with DietPi OS. With the unmodified picochess.ini, after boot when PicoChess was running and connected to a DGT BT board with the pieces in the starting position and comparing using htop, there isn't much difference.
DietPi Lite
Mem: 572MB 589MB
Swp: 0K 100K
Load Average: 0.37 0.38 0.24 0.13 0.14 0.09
Running StockfishNN at full strength (Elo 3190, 3 threads) in analysis mode (FEN 8/3P3k/n2K3p/2p3n1/1b4N1/2p1p1P1/8/3B4 w - - 0 1) for 5 minutes:
Mem: 621MB 638MB
Swp: 0K 1.46MB
Load Average: 3.49 2.17 1.04 3.21 2.36 1.14
Temp: 73.0C 64.5C
Stop PicoChess. Allow temp to get below 60C. Benchmark StockfishNN twice:
38550/38558 nps 40004/39951 nps
So, I would say no compelling reason to switch the underlying distro to DietPi.
For those curious, here are the numbers when using the PicoChess v3.3 Desktop image in a stock DGTPi with a 2 GB swap file and monitor attached (not an easy task to get running - waited many minutes after boot before PicoChess was ready and many more minutes before the Chromium kiosk mode started):
Desktop Image on DGTPi
Mem: 435MB
Swp: 638MB
Load Average: 0.27 0.66 1.50
Running StockfishNN at full strength (Elo 3190, 3 threads) in analysis mode (FEN 8/3P3k/n2K3p/2p3n1/1b4N1/2p1p1P1/8/3B4 w - - 0 1) for 5 minutes:
Mem: 658MB
Swp: 465M
Load Average: 4.24 3.60 2.69
Temp: 80.6C
Stop PicoChess. Temp wouldn't go below 60.1C even with Chromium closed on desktop.. Benchmark StockfishNN twice:
32439/32475 nps with Chromium open
32787/32708 nps with Chromium closed (only slightly better)
Needless to say, the Desktop image is not recommended on a stock DGTPi. It really benefits from more memory and faster processor (i.e. Pi4b or better).
Randy