My main use of 12v is running my fridge but, by design, the compressor will not cut-in unless there is at least 11.7v available, consequently, allowing for a bit of voltage drop in the cables, etc, only around 50-60% of the battery's capacity is available to me for my primary application - lithium would give me closer to 100%
Yes, if you’re getting down to 11.7v then you must be running your batteries right down to the limit (and/or have some really nasty voltage losses on your cabling). Lithium would give you more Ah-for-Ah capacity. Also, sticking in another AGM would do the same. Like every other scenario, carefully assessing the cost/weight/size/capacity trade-off in your application should make it clear the way to go.