Okay, I took your suggested numbers for your party but ended up in a different place than you did. Help me review:
Bladesinger, DEX 18 -- 1st round prep, then BB for 2d8+4 with a +7 attack bonus
Archer fighter, DEX 18 (I upped this from your 16?) -- using sharpshooter, 2 attacks, d8+14 each at +2 attack bonus
Rogue, DEX 18 )again, upped from 16?) -- no sneak first round so d6+4, sneak thereafter for 5d6+4, +7 attack bonus
Cleric, WIS 18 -- 1st round prep, cast sacred flame after for 2d8 DC 15 (giant's fail 75% of the time)
So, from that I get:
round 1
Bladesinger 0
Cleric 0
Archer: 19.4 (37 * .4 + .1 * 46)
Rogue: 5.8 (7.5 * .7 + .05 * 11)
Total damage dealt (ave): 25.2
Round 2 (and thereafter)
Bladesinger: 10.2 (13 * .7 + .05 * 22)
Cleric: 6.75 (9 * .75)
RogueL 16.65 (21.5 * .7 + .05 * 39)
Archer: 19.4
Total damage dealt this round: 53
Round 1 total damage: 25.2
Round 2 total damage: 78.2
Round 3 total damage: 131.2 (1st giant dead)
Round 4 total damage: 184.2
Round 5 total damage: 237.2 (2nd giant dead)
Bladesinger party takes 5 rounds, with 2 rocks +4 clubs +4 clubs +2 clubs +2 clubs or 14 attacks a combat, not 12? I guess this depends on initiative? 12 is good.
A champion party with a greatsword champ, same rogue, same cleric (but casts spiritual weapon that attacks 1st in round 2 instead of warding bond), wizard that searing ray and magic missiles before flame bolting will end this same fight on round 4 instead of 5 taking 2 rocks, 4 clubs, 2 clubs, 2 clubs or 10 total attacks. Accounting for Champion crits and extra attack, they almost kill a giant in round 2. A magic weapon for the champion seals this deal handily and reduces total attacks to 8.
A champion party with sword and board defensive still, otherwise same as above barely edges out the giants in 4 rounds, and it's unlikely that they exactly match the first giant's hp's and apply everything after immediately to the second giant, so let's go with 5 rounds for this group as well. The greatsword group handily deals enough damage, so even a 1 hitpoint greatsword hit doesn't change their math.
So, then, how many hits is an AC 18 greatsword champion expected to take over 32 attacks?
6 hits....~100.00%
7 hits.......99.09%
8 hits.......97.52%
9 hits.......94.25%
10 hits......88.44%
11 hits......79.54%
12 hits......67.67%
13 hits......53.82%
14 hits......39.61%
15 hits......26.76%
16 hits......16.48%
My spreadsheet was built to provide chance for up to 16 hits on the assumption that would be plenty. I think that holds.
So, 2:3 to take 12 hits, 1:2 for 13. Let's assume 3 hits per fight. Average damage is 18.5 for 55.5 damage. The fighter doesn't drop in any given fight, but after first fight a second wind (11.5 hp healing, remainder 44) and cleric can burn their channel for 30 of that, leaving 14. Can't carry that into the second fight, without dying, so a 1st level heal will cure 8.5, leaving 5.5. Next fight ends with champ down 61 hps, very close to dropping. Short rest, burns 3 hit die for 30.5 healing, down 30.5 now. Cleric uses second channel, healed. Cleric now at 3/1/3. 3rd fight, comes out down 55.5 damage. Second wind heals 11.5, down 44. Cleric casts 2 cure wounds at 1st for 17, leaves 27. Not good enough. Another gets us to 19.5, will need a 3rd slot to get to the last fight. Cleric is down to 0/0/2 going into the last fight. Last fight cleric uses a 3rd for spiritual weapon, champion survives with 55.5 damage, long rest.
Greatsword champion comes out slightly worse than the Bladesinger in total party resource burn. If I add in action surge in two fights, the increase in damage takes out a giant one turn faster and reduces total damage taken by enough to get into parity with the bladesinger party. Neither party is particularly good at damage out (I think you shorted your bladesinger by using booming blade). Both have resources left for the wizard/cleric to use a 3rd slot for exploration purposes. It seems a wash between damage out and damage in.
The sword and board champion, however, is a clear loser to the Bladesinger.
ETA: I figured both archers as champion archers, and just realized at the end that you specified a battlemaster archer using precision. Damage for bladesinger party goes up accordingly and the Bladesinger party does defeat the giants in 4 turns, not 5. However, the effectiveness of a battlemaster over a champion fighter, especially with SS/GWM and precision, has been beaten to death and clearly shown on these boards. I think to be as fair a comparison as possible, if the bladesinger is being compared to a champion, that the bladesinger party have a champion and not a battelmaster to make the comparison even. That way, it's as similar as possible for comparison: bladesigner party is wizard (bladesinger), cleric (life) rogue (AT), fighter (champion) and the Champion party is: fighter (Champion), wizard (unspecified), cleric (life), and rogue (AT). The only difference then is changing the tradition of the bladesinger and changing the champion and wizaard from a melee role to a ranged role.
ETA2: the sword and board champion still loses to the bladesinger with similar parties, so it's still a clear win for team Bladesinger.