Language theoretic comparison of LL and LR grammars
There are numerous containments known. Let $\subseteq$ denote containment and $\subset$ proper containment. Let $\times$ denote incomparability.
Let $LL = \bigcup_k LL(k)$, $LR = \bigcup_k LR(k)$.
Grammar level
For LL

$LL(0) \subset LL(1) \subset LL(2) \subset LL(2) \subset \cdots \subset LL(k) \subset \cdots \subset LL \subset LL(*)$
$SLL(1) = LL(1), SLL(k) \subset LL(k), SLL(k+1) \times LL(k)$

Most of these are proven in Properties of deterministic top down grammars by Rosenkrantz and Stearns. $SLL(k+1) \times LL(k)$ is a rather trivial exercise. This presentation by Terence Parr places $LL(*)$ on slide 13. The paper LL-regular grammars by Jarzabek and Krawczyk show $LL \subset LLR$, and their proof trivially extends to $LL \subset LL(*)$
For LR

$LR(0) \subset SLR(1) \subset LALR(1) \subset LR(1)$
$SLR(k) \subset LALR(k) \subset LR(k)$
$SLR(1) \subset SLR(2) \subset \cdots \subset SLR(k)$
$LALR(1) \subset LALR(2) \subset \cdots \subset LALR(k)$
$LR(0) \subset LR(1) \subset LR(2) \subset \cdots \subset LR(k) \subset \cdots \subset LR$

These are all simple exercises.
LL versus LR

$LL(k) \subset LR(k)$ (Properties of deterministic top down grammars plus any left recursive grammar)
$LL(k) \times SLR(k), LALR(k), LR(k-1)$ (simple exercise)
$LL \subset LR$ (any left recursive grammar)
$LL(*) \times LR$ (left recursion versus arbitrary lookahead)

Language level
For LL

$LL(0) \subset LL(1) \subset LL(2) \subset \cdots \subset LL(k) \subset \cdots \subset LL \subset LL(*)$
$SLL(k) = LL(k)$

Most of these are proven in Properties of deterministic top down grammars. The equivalence problem for LL- and LR-regular grammars by Nijholt makes references to papers showing $LL(k) \subset LL(*)$. The paper LL-regular grammars by Jarzabek and Krawczyk show $LL \subset LLR$, and their proof trivially extends to $LL \subset LL(*)$
For LR

$LR(0) \subset SLR(1) = LALR(1) = LR(1) = SLR(k) = LALR(k) = LR(k) = LR$

Some of these were proven by Knuth in his paper On the Translation of Languages from Left to Right in which he introduced LR(k), the rest are proven in Transforming LR(k) Grammars to LR(1), SLR(1), and (1,1) Bounded Right-Context Grammars by Mickunas et al.
LL versus LR

$LL \subset LR(1)$ (containment follows from the above, $\{ a^i b^j | i \geq j \}$ is the canonical example for strict containment)
$LL(*) \times LR$ (the language $\{ a^i b^j | i \geq j \}$ shows half the claim, and the introduction of The equivalence problem for LL- and LR-regular grammars by Nijholt makes references to papers showing the other half)
$LR(1) = DCFL$ (see e.g. reference here).