Like the others, it’s mostly convenience. Free teleports do save you time/shards if you are trying to find things like legend entries or during an event when you want to go on the open raid and then get back to missions.
The cache keys are nice, although you won’t be able to use the distillates fully early on as they tend to come in 5000xp and up (not really sure of the minimum since it has gone up over time and I’m not sure if that’s Funcom increasing it for everybody or if it’s just that the minimum goes up as your character gains in power). This will more than get a green item from base to max level.
They are much more useful later on because they empower with no anima shard cost. This is not so important with green items, but it becomes much more important when you’re trying to empower Mythic (yellow) gear.
The cosmetics and extraordinary weapons/talismans from the caches can be bought on the auction house - although if you’re not a patron you have to visit the auction house in Agartha to pick them up (more time convenience, since a patron gets drone item delivery).
You get a bonus on XP and anima shard rewards for mission completion, which is a subtle boost.
For buying stuff on the auction house, you get a bonus to Marks of Favor rewarded for completing daily
challenges - also a time convenience.
If/when you decide to run dungeons/lairs/scenarios, you get one daily bonus key of each type, so that’s an extra reward.
To sum up, you get things done faster and level up faster if you are a patron. You don’t get anything that you can’t eventually get if you’re not, although the wait may be a long one.