Tolkien spoke to this in his letter #33 to his publishers at Allen and Unwin, noting that the tone of LotR is substantially darker and "older" than that of the Hobbit:
In the last two or three days, after the benefit of idleness and open
air, and the sanctioned neglect of duty, I have begun again on the
sequel to the ‘Hobbit’ – The Lord of the Ring. It is now flowing
along, and getting quite out of hand. It has reached about Chapter VII
and progresses towards quite unforeseen goals. I must say I think it
is a good deal better in places and some ways than the predecessor;
but that does not say that I think it either more suitable or more
adapted for its audience. For one thing it is, like my own children
(who have the immediate serial rights), rather ‘older’. I can only say
that Mr Lewis (my stout backer of the Times and T.L.S.) professes
himself more than pleased.
In Letter #34, he professed that he felt that LotR would be "terrifying" to younger children who might have enjoyed the earlier Hobbit book:
When I spoke, in an earlier letter to Mr Furth, of this sequel getting
‘out of hand’, I did not mean it to be complimentary to the process. I
really meant it was running its course, and forgetting ‘children’, and
was becoming more terrifying than the Hobbit. It may prove quite
unsuitable. It is more ‘adult’ – but my own children who criticize it
as it appears are now older.
and in his letter #131 he spoke to the major change of style:
The generally different tone and style of The Hobbit is due, in point
of genesis, to it being taken by me as a matter from the great cycle
susceptible of treatment as a ‘fairy-story’, for children. Some of the
details of tone and treatment are, I now think, even on that basis,
mistaken. But I should not wish to change much. For in effect this is
a study of simple ordinary man, neither artistic nor noble and heroic
(but not without the undeveloped seeds of these things) against a high
setting – and in fact (as a critic has perceived) the tone and style
change with the Hobbit’s development, passing from fairy-tale to the
noble and high and relapsing with the return.
and in his letter #163 to W.H. Auden he criticises some of the writings in the hobbit as being both juvenile (in style) and juvenilia:
I went on after return; but when I attempted to get any of this stuff
published I was not successful. The Hobbit was originally quite
unconnected, though it inevitably got drawn in to the circumference of
the greater construction; and in the event modified it. It was
unhappily really meant, as far as I was conscious, as a ‘children’s
story’, and as I had not learned sense then, and my children were not
quite old enough to correct me, it has some of the sillinesses of
manner caught unthinkingly from the kind of stuff I had had served to
me, as Chaucer may catch a minstrel tag. I deeply regret them. So do
intelligent children.
and if you want a more detailed (and wildly harsh) critique of his own works, you can't really do better than his Letter #215 to Allen and Unwin (refusing to attend a symposium on "writing for children":
When I published The Hobbit – hurriedly and without due consideration
– I was still influenced by the convention that ‘fairy-stories’ are
naturally directed to children (with or without the silly added
waggery ‘from seven to seventy’). And I had children of my own. But
the desire to address children, as such, had nothing to do with the
story as such in itself or the urge to write it. But it had some
unfortunate effects on the mode of expression and narrative method,
which if I had not been rushed, I should have corrected. Intelligent
children of good taste (of which there seem quite a number) have
always, I am glad to say, singled out the points in manner where the
address is to children as blemishes... The relation between The Hobbit and its sequel is I think this. The Hobbit is a first essay or introduction (consideration will admit I think that it is a very just point at which to begin the narration of the subsequent events) to a complex narrative which had been brewing in my mind for years. It was overtly addressed to children for two reasons: I had at that time children of my own and was accustomed to making up (ephemeral) stories for them; I had been brought up to believe that there was a real and special connexion between children and fairy-stories. Or rather to believe that this was a received opinion of my world and of publishers. I doubted it, since it did not accord with my personal experience of my own taste, nor with my observation of children (notably my own). But the convention was strong.
I think that The Hobbit can be seen to begin in what might be called a more ‘whimsy’ mode, and in places even more facetious, and move steadily to a more serious or significant, and more consistent and historical. . . . . But I regret much of it all the same. . . . .