It is obvious, if a transformer is outperformed at all points by another, it will be replaced by that one. This was the case with LL9206, which is a fine transformer by itself. It was made since very many years, but the newer LL9226 was just better. LL9206 is still made, but not recommended for new designs any more. All other transformers in the program, have their own justification, and it's best use is where this justification is needed. This is text is a little help when selecting.
First, you need to keep apart the small size and large size transformers.
Small size series: LL1636, LL1678 and LL9226(XL). A good core is very expensive by the weight, and so is the mu-metal which is used for shielding. Since signal level of MC transformers is low anyway, a small core can be used easily. Yet the small size results in slightly less frequency range, whereas this is far outside the audible range. They all have the expensive Cobalt cores, which becomes more affordable at the smaller size. All in all, these have an amazingly good price performance ratio. The LL9226-XL is a larger version of the popular LL9226, and it comes closer to the larger size transformers.
Large size series: LL1931, LL1933, LL1941, LL1943, LL1971. The larger core gives more room. This allows the use of thicker wire, resulting in less loss, and an extended frequency range. This reflects however in the price. Also these series have the choice of amorphous nickel, or amorphous cobalt. In addition silver wire is possible with some types. The copper wire is oxygen free, 9999.99% pure (6N) Cardas branded wire.
Large type: LL1681. This transformer has a mu metal core, which gives as little sound coloring as possible.
Large size series is: LL1961, LL1963. These are special types with a low transfer ratio. Not extremely common, but some special cartridges need that.
Shield advantage: The shield splits primary to secondary capacitance in two, and in between is now this shield. Since the shield is grounded, this makes it impossible for an electric hum field, to pass this. It is literally: A shield. In electronic terms, the primary and secondary windings are now each inside a it's own cage. That is why this is also called sometimes a Faraday cage. Sure this works really excellent. When to use it? In situations, where hum is an issue, some small loss of efficiency can be sacrificed for this. For that it is free of hum. If hum is not a known issue in your set up, the unshielded version may have slightly better overall performance.
Silver wire. The conductivity of silver is slightly better. Also the metal crystals are larger. These two things are the facts, and the rest is opinion. Copper is said to sound warmer, and silver is said to sound brighter. If you ask on a forum, most have never compared the sound in reality, while still explaining others what they need to know. For sure, I can say there is a high interest in silver wound transformers. I can tell from the email request and the phone calls. But people hesitate a lot, when they hear the transformers cost appr. 5x more, and in the end most users go for copper wire transformers. Still, afterwards those few who go for silver, usually will give me feedback, and it is always very positive. No customer ever told me it was not worth it.