20 BGs are comparable to 30 Execs in a figth (and 60 pts cheaper), but as 20 is the maximum size of BGs they make a poor large unit.
30 Execs (3x10) Vs 20 BG (2x10):
This is a misleading matchup:
30 Execs = 360 points
20 BG = 260 points
If you're going to do a point comparisson match up, then you need to go with equalish values. Otherwise I'll give you a matchup of 10,000 goblins against your 20 Blackguard and conclusively prove that goblins are better.
I see your point about being allowed a max of 20 BG, but if you're going to insist on using 30 Execs then you can boost the points cost of the BG to be even through other ways.
A more appropriate matchup would be:
20 BG (10/10) with FC, Crimson Death and Banner of Murder (345 points) versus 30 Execs (10/10/10) (360 points).
Now lets do the comparisson:
CC Round one:
BG R&F:
28 WS5 attacks (18 from front rank, 10 from back rank) = 21 hits (14 initially, then 7 more from warrior elite)
21 hits = 14 wounds (S4 vs T3 = 3s to wound)
14 wounds = 14 dead (S4 and AP = -2 modifier versus exec's 5+ armour save = no save).
BG Champion
3 WS5 attacks = 2.25 hits (1.5 initially, then 0.75 more from warrior elite)
2.25 hits = 1.875 wounds (S6 vs T3 = 2s to wound)
1.875 wounds = 1.875 dead (S6 and AP = -4 modifier versus exec's 5+ armour save = no save).
Total: 16 dead (rounding up from 15.875)
The 14 remaining R&F Execs strike back:
14 WS5 attacks = 10.5 hits (7 initially, further 3.5 from hatred).
10.5 hits = 8.75 wounds (S6 vs T3 = 2s to wound)
8.75 wounds = 8.75 dead (S6 = -3 modifier versus BG 5+ armour save = no save)
Total: 9 dead (rounding up from 8.75)
So, at the end of round one, you have 14 Execs left and 11 BG. Execs have the same number of ranks as the BG, so are not stubborn, but may still (barely) pass their break test.
Assuming they stick around, lets move on to:
CC Round two:
BG R&F
BG strike first with 19 WS5 attacks (18 from front rank and 1 from rear rank) = 14.25 hits (9.5 initially, followed by 4.25 from hatred.
14.25 hits = 9.5 wounds (S4 vs T3 = wounding on 2s)
9.5 wounds = 9.5 dead (S4 and AP = -2 modifier versus exec's 5+ armour save = no save)
BG Champ
3 WS5 attacks = 2.25 hits (1.5 initially, then 0.75 more from warrior elite)
2.25 hits = 1.875 wounds (S6 vs T3 = 2s to wound)
1.875 wounds = 1.875 dead (S6 and AP = -4 modifier versus exec's 5+ armour save = no save).
Total: 11 dead (rounding down from 11.375)
The three remaining execs hit back
3 attacks = 1.5 hits (4s to hit, and now no hatred as second round of CC)
1.5 hits = 1.25 wounds (S6 vs T3 = 2s to wound)
1.25 wounds = 1.25 dead (S6 = -3 modifier versus BG's 5+ armour save = no save)
Total: 1 dead (rounding down from 1.25)
At the end of round 2, the Execs have three remaining versus the BG's ten. There's no way that they will pass their break test as they're no longer stubborn and lost combat by a mile. Of course its possible that they roll snake eyes and stay, but then you've got 10 BG with death wielding champ versus 3 ASL Execs. It's a no brainer what happens even if they do not run...
Convincing win: BG
But, with match ups of this kind, you miss out on a lot of the more important aspects of unit value, including their non-combat advantages (e.g. the BG are ITP and auto stubborn, can take magic items and can take bigger magic banners), their potential synergies with other units (e.g. BG can include non-khainite characters - including mages - whereas execs cannot), match up against other creatures (Execs are way better against high toughness, high armour creatures, whereas BG are awesome at low-mid level toughness and armour killers) and other factors.