I've never had a caique or a rainbow lorikeet, but I have had two purple crowned lorikeets in my lifetime. Purple crowns are everything that the bigger lorikeet species are, just on a smaller and more manageable scale.
Lorikeets and caiques are both very smart. They both are SO smart that they do not do well if they are stuck in their cage all day, or if their human flock is absent from the house for long periods of time. Because they're so intelligent they quickly become bored and lonely which could lead to self-destructive habits like feather plucking or even self mutilation. Of the two species I would suggest caiques might be a little easier to keep given they don't have the kind of specialised dietary requirements that lorikeets do, to say nothing about their liquid projectile poop! Many owners of lorikeets do not understand hygiene standards that are involved with them and lose them to bacterial infection if those standards are not met. The other issue, apart from initial cost of purchase, is the cost of ongoing veterinary care which is generally more expensive for birds than your average dog or cat.
Lorikeets are hysterically funny excitable little goofballs but can easily be over-stimulated into undesirable aggressive or hormonal behaviours. This is the main reason why I have always stuck to the smaller species - my little Lilly is smaller than a budgie but when her hormones are raging she can bite very hard indeed, *almost* to the point of drawing blood. An associate of mine about 20 years ago had a rainbow that became extremely bitey upon maturity and was inflicting some real damage with his beak, so she decided to get him a mate. Let's just say her biting troubles only doubled when a second lorikeet was introduced!
Rainbow lorikeets are funny, endearing, playful little fuzzballs that can become mad, bad and dangerous to know in the blink of an eye, and can inflict quite serious and deep wounds with their very sharp beaks. They can undergo a complete change in personality once they reach sexual maturity. Some owners have reported their rainbows have become so aggressive that they need to either rehome them or build them an outdoor aviary and possibly even get them an opposite-sex mate because they simply cannot handle them as an indoor pet anymore.
I have included a link for you which will give you an idea of the good, bad and very ugly of lorikeet behaviour ...
The Lory Link
I'm sure other members will be along soon to advise you on the finer points of caique ownership too.
I wish you the best of luck with your decision.