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Chessgi and Shogi have the highest resistance to computer analysis because
the drop rule gives them a HUGE branching factor, at least in the
mid-game, once several pieces are in-hand.  Most would probably suspect
Chessgi to have a larger branching factor than Shogi, because the Chess
pieces are so much more powerful, and thus have many more possible moves. 
I suspect that Shogi, however, actually has the larger branching factor due
to the fact that the board has 81 squares instead of 64.  In any case,
these games won't be 'digestable' by computers for several decades at
best, in my opinion.  They are both still easy to analyze very deeply in
the opening, though, with Shogi being a little more so, because pieces
aren't usually captured quite as early as in Chess.  Shogi is a wonderful
game to be sure; I haven't played Chessgi, but I suspect it is wildly more
challenging (for a human) to play than Shogi.

An interesting question would be how resistant to computer analysis
Marsellias Chess (or other double-move games) would be.  ChessV doesn't
support any double-move games at present, and I must confess that I am not
at all clear on how to program such a thing efficiently.  I have found no
technical writings on the subject.  The only computer program I know of
that plays such games is Zillions-of-Games, so the Zillions team might
well be the only people on the planet who know anything about it.  And
their solution wouldn't really be directly applicable, anyway, even if
they wanted to share it.  Although I know none of the technical details of
how Zillions is programmed, I am quite certain that it is of a radically
different design than ChessV.  This is primarily because the two programs
were written with a very different design goal.  Zillions is designed to
play as many games as possible (currently hundreds, if not thousands, but
many are played very poorly.)  ChessV is designed to play as many games as
is possible to play with a very high level of skill (presently about 35;
will be hundreds, but many chess variants will NEVER be supported.)  I
will investigate double-move some day, but I have about a thousand other
things I want to do first.

Now, the super-computer resistant game is Go, with 19 x 19 = 361 legal
opening moves ...  Ok, you can divide by four (at least) because of the
symmetry, but after a few moves, the board will be asymmetric, and the
branching factor will still be 300+!!!   Computers play Go very badly ... 
I got the best program I could get about 3 years ago and was able to beat
it, even giving it quite a long time (which is scarry, because I'm really
not very good; about 15 kue at best.)  I'm sure programs have gotten
somewhat better, but I know for a fact that there are literally thousands
and thousands of kids living in China/Japan/Korea less than ten years old
who can easily defeat the best technology has to offer.