Uhm... SH Siege get you soul shards if you manage to make kills, but it is limited to the number of attackers based on the level of your Tower of Odin. It's all fixed and there is a maximum you can earn.
In Holmgang you get three rounds of 15min to destroy 3 fortresses per turn. It's not difficult to destroy at least one every turn, depending on the level. If you are strong enough you can destroy two or three per turn. There's 10 to 20 times more troops in every fortress than in a wave of Siege tower lvl 1. Catching 10m soul shards is really not difficult.
I hope this clarifies that Holmgang is needed for faster growth. Unless you don't know about the millions of soul shards needed to raise each of your buildings after lvl 35 of course. In that case you know now.
Yes I know about SH siege ... it is just that you mentioned it in your OP so it confused me if that had anything to do with Homgang ... and yes I do realize about the need for soul shards ...