Hot to test 16-bit numbers in assembler?

Are you sure? This example works quite well:

org #4000
ld hl,4000
ld de,3000
or a
sbc hl,de
jp z,equal
jp p,positive
jp m,negative
ret

equal ld a,0
ret

positive ld a,1
ret

negative ld a,-1
ret

Better to test carry in stead of p/m, otherwise if de is large you will not get the result expected:

ld hl,4000
ld de,3000
or a                  ; this resets carry so sbc doesn’t deduct one extra
sbc hl,de
jr z,hl_equals_de
jr c,hl_lessthan_de
jr nc,hl_greaterthan_de

To test >=, simply remove the jr z and use the jr nc (as nc includes zero).
To test <=, you can replace the or a by scf (deducts 1 more) and then jr c.

SBC means "subtract with carry". So, SBC HL,DE -> HL = HL - DE - CY. Unfortunately there's no SUB HL,DE instruction, so if you just want to get HL=HL-DE then you have to use SBC HL,DE with a non-set (i.e. 0) carry. Using the OR A instruction before clears the carry flag.

One way is to add 8000H to both values before doing the test.

(Note that instead of actually adding 8000H, you can add 80H to h and d, or just toggle bit 7 of h and d.)

Nice! I like to use BIOS when possible.