Why do Greek and Cyrillic have different collation order than Roman alphabet?

The collation of Greek and Roman are pretty similar, as Philip said, once you factor out archaisms, and the tendency to insert new letters at the end of the alphabet.

The original Roman alphabet matches to the original Greek alphabet pretty well:

A Α
B Β
C Γ
D Δ
E Ε
F Ϝ
G —
—  Ζ
H Η
— Θ
I ~ J  Ι
K  Κ
L Λ
M Μ
N Ν
— Ξ
O Ο
P Π
Q Ϙ
R Ρ
S Σ
T Τ
U ~ V Υ
— Φ
— Χ
— Ψ
— Ω
X (Ξ)
Y (Υ)
Z (Ζ)

The Greek equivalents of F and Q fell out of use. J and V are variants of original I and U, and appended after them. W, when it developed, was a variant of V, and appended after it. Ζ, Θ, Ξ, Φ, Χ, Ψ, Ω were left out of the original Roman alphabet—although as it turns out, Χ in the western Greek alphabet corresponded to Ξ in the eastern, so it was in the right kind of place. X, Y, Z were imports from Greek, and stuck on the end.

The only real oddity is G and Ζ being in the same position. G was invented in the Roman alphabet as a variant of C; the theory is that it was slotted in where Greek Ζ used to be, precisely because Greek Z had dropped out after F. See G

Cyrillic patterns closely to Greek too, if you allow for variants of letters being inserted in place, and new letters being appended at the end.

See early Cyrillic alphabet:
А Α
БВ Β
Г Γ
Д Δ
Е Ε
ЖЅЗ Ζ
И Η
— Θ
І Ι
К Κ
Л Λ
М Μ
Н Ν
— Ξ
О Ο
П Π
Р Π
С Σ
Т Τ
Ѹ Υ
Ф Φ
Х Χ
— Ψ
Ѡ Ω
ЦЧШЩЪЫЬѢЮꙖѤѦѨѪѬѮѰѲѴҀ

Б was inserted as a variant of Β. Ж and Ѕ were inserted as variants of З = Ζ. Θ, Ξ, Ψ were left out as unnecessary to Slavic, though there were then re-appended at the end, to transliterate Greek:  ѮѰѲ. In fact the very last letter appended, Ҁ, was appended for Greek numerals: ϟ, koppa (which earlier looked like Ϙ).