Ulric's plan for the invasion of Rasalhague pit a single cluster backed by the Golden Keshik against the Free Rasalhague's best mech regiment, the surviving battlaion of a second top regiment, a newly formed regiment of light mechs (likely militia quality material & refurbished trainers), two regiments of armor, and five regiments of mechanized infantry. This would be old school mechanized infantry, troops traveling about in Goblins, APCs, Maxims, and other IFVs & ISVs.
To avoid the oversized elite Flying Drakons of the 1st Drakons, Ulric landed the mechs and dropships supporting those two commands 200 klicks north of the capital of Reykjavik. The Rassies though the Wolves had made a mistake because the other two clusters involved in the invasion landed near their objectives and proceeded to smash the defenders despite prepared ambush positions. The Golden Keshik & 4th Wolf Guards marched south, somewhat protected by the mountains and forests of their chosen axis of advance, limiting the ways ASF could attack ground targets. I would imagine the two formations having 45 Gargoyles out of 55 mechs let the LB-5xs of the Primes keep the ASF away too- per WCSB 9 of the Gargoyles were Primes on Tukayyid (though that should not have mattered for a long battle) which is a clue to their ratios for longer battles.
The defense's general ordered the capital's defenders north 75 kilometers to establish a new defensive line on the south side of a river with more forested mountains at their back. The Keshik & 4th were working their way south as the other two cluster pushed the defenders back into the objectives. By the time those defenders had fallen back to prepare for a last stand, the Keshik & 4th had started to hammer at the capitals defenders. Knowing that when those last stands were finished the Invasion Wolves would shift forces to finish the capital, the defending general ordered his forces to break contact and fall back to their previous prepared positions.
This is where Ulric's skill shows through . . . his 'mistake' let the capital's defenders absorb the news their fellow soldiers on planet were getting taken out. Both Drakon formations, the vet's light regiment, armor and infantry were all faced with what seemed like inevitable defeat- especially since with overwhelming numbers they had not managed to stop the 4th Wolf Guards & Golden Keshik. Also knowing from Phelan that Magnusson was a guerilla who managed to escape being trapped by Kuritans several times, the Wolves left a way out for the Republic's leader. With the other two defense points about to fall, the Wolf forces to the north not being stopped despite the numbers, Magnusson fled under the protection of the elite Flying Drakons.
The most dangerous group of defenders was removed from the board, the other two victorious clusters would be able to shift to assist mopping up the remaining defenders without having to worry about ASF attacks on their dropships, and rather than facing civilians & troops enraged by the loss of their leader the Wolves faced demoralized but fanatical defenders.
The Golden Keshik & 4th Wolf Guards had during their push south taken out over a battalion of mechs and undisclosed numbers of conventional forces. Which is impressive considering they were very outnumbered though Ulric and Jera Carns had a massive equalizer in her cluster- the Command Trinary. The command trinary had two artillery stars . . . which means 10 Naga, or 20 Arrow IVs that could be dropped on targets. It is hard to imagine the elite (what WCSB says) artillery stars not being used to blast a 20 A4 hole in the Rassie's defensive lines set up just south of that river- especially as the Wolf forces being nearly all Gargoyles are not equipped with jump jets. Blow a hole in the lines to the left or to the right of whatever crossing Ulric & Star Colonel Jera Carns selected, Gargoyles ford the river crossing carrying Elementals. The twenty-four points of Elementals are dropped in the Rassie lines to tie up defenders while the 4th Wolf Guards mechs finish punching through the lines and then hook left or right as the case maybe to clear the bridge of defenders. Some Elementals clear the bridge of spoiling charges after the mechs took out the strong point of (IMO) armor & infantry guarding that approach and thus they can get their logistical trail across the river.
The Invasion Wolves fielded 55 Omni-Mechs, mostly Gargoyles, 10 Naga for artillery, 24 Elemental points, and 26 ASF for the advance south from the Asgard LZ. The Free Rasalhague Republic forces defending Reykjavik fielded around 144 frontline mechs, 108 light mechs in the recently raised old vets regiment, over 200 armored fighting vehicles, and the 5 regiments of mechanized infantry which would have a large number of IFV/ISV. Most likely not all the armor & infantry would have been sent north to form the defensive line between Asgard and Reykjavik, it would depend on how built up the road net was to support those forces 75 kilometers from their prepared positions with established supplies.
Despite the tech and weight advantage the Wolves would have, it is nearly a 5-1 ratio in mechs for the defenders, no armor, and a much higher ratio for the Elementals (like 1 Elemental point would need to kill a infantry battalion for parity). The Invasion Wolves would have a edge in the mobility and firepower of their artillery since WCSB says the Rassies have some but does not specify- figure some in the armor and infantry regiments. The Wolf aero was held in reserve to follow Magnusson out.
The BV for the match up is probably pretty balanced . . . the elite Wolf omnimechs are around 5-5.5k BV each and Elemental points around 800-900 BV, giving a ballpark BV for combat forces around 322k w/o the Nagas or ASF. Compare the FRR forces where a mech might average 1.1k due to at least two-fifths of the Rassies being lights like Panthers, Jenners, Commandos and bug mechs for a total of 302k. Two regiments of armor- even if they are just Vedettes & Scorpions- which is unlikely since this is the capital- should generate another 120k of BV easily . . . thus, strategically a BV balanced fight.