Indeed most of the windings are on the primary.
Generally you are advised to use the highest ohmage tap to employ as much of the secondary as possible. Conventional wisdom suggests that the amp sounds better when this is done, however I don't really have an opinion on this either way as it is very difficult to make a sensible comparison.
To make the correct comparison you would first have to ensure the load is correctly matched. I personally think that valve amps sound best when the load is correctly matched, as does everyone who I've had a chance to test this with. I was chatting recently to Andy Marshall of THD electronics (who REALLY knows what he is doing) and he also concurs with this view.
Thus if you have a 16 ohm series parallel 4 x 12 cab it will of course sound different (and almost certainly better) when connected to the 16 ohm tap than the 4 ohm tap. You could of course rewire the cab for 4 ohms and it will probably sound better on the 4 ohm tap, but you now have a cab wired with all 4 speakers in parallel. This will course sound different to a 16 ohm cab wired in series parallel regardless of any transformer utilization. So as you can see (hear!) to do a worthwhile comparison is hard, and when someone says they prefer the sound of a Marshall run at 16 ohms you really have to know what exactly they are doing before you can draw any conclusions.
To further complicate matters, you also need to consider how the transformer is wound. For example Hammond wind most of their transformers so you will use virtually all the secondary whatever load you match. You can also wind a transformer with secondary windings that can match 4 and 16 ohms whilst using all secondary windings. So secondary usage is less of an issue with this style of transformer, although winding topology may be.
Many vintage repro Marshall transformers are made with unused windings eg a 100 V line secondary, or 9K primary windings in the case of the old RS-style JTM45 output transformers. Many people think that this affects the sound of the transformer, although my guess this is due to the topology of the windings as a result of having the extra taps rather than any effects of the unused windings, although to tell the truth there probably isn't a definitive answer to this.
My advice to you would be to try the speakers in series and parallel attached to the appropriate taps and use whichever you prefer.
By the way vintage Fender Twins only have single secondary winding which matches the amp to 4 ohms, so as you are using all the secondary windings which tap you should connect to is not an issue.
