Mystique winning isn't too farfetched if we're assuming she isn't going on direct assault.
Regardless of her manifested size, Mystique retains her normal weight, so bulkiness of her form is not too much of an issue.
As shown during her term with X-Factor, she can manifest certain abilities of other super powered beings as she did when she showed she can fly by morphing Angel's wings on her back (projectiles, mental, etc. she cannot however). She can also add addition portions to specific parts of her own body, such as spikes, etc. as demonstrated when she engaged Dark Beast. Lastly, she can manifest into non-humoid forms such as an animal (i.e. she changed to a wolf when she fought Sabertooth once) or an anonymous creature type.
However, regardless of what form, she doesn't inherit the same durability (i.e. she morphed into a soldier with a bullet-proof vest, but the bullet-proof vest didn't nearly nearly do as good a job as a real one).
In the fight, I can see her turning herself into Betty to have Hulk defend her from Juggernaut, or she can always camoflage herself by blending with the environment. She cannot defeat Juggernaut, but if Hulk managed to take down him, she can kill Hulk later if and ever he changes to human.
Yes, she definitely doesn't stand a chance if fighting directly. She couldn't even handle Sabertooth let alone these two heavyweights in that regard.
And thanks about the avatar. I was looking for an image of a character with a radio and the closest I could think of was Kero with a walkie-talkie in a scene of Cardcaptor Sakura, which I scanned in.
Mystique is not a dedicated fighter. She uses her metamorph abilities for mind games, stealth, etc. If going by powers alone, yes she will get herself slaughtered by them easily. But part of her criteria when engaging a battle is trickery and Hulk's an easy target for this especially. I cannot see anyone Juggernaut closely respects to stop an engagement, unless we are to say Black Tom.
Even if going by Hulk with Bruce's brain, you will be surprised how hard people take to convince themselves of what they're seeing is not what it appears. But true, if with Bruce's brain, he would most likely not be as susceptible, but the sight would still disturb him in raising a hand at her in a Betty or even Rick form.
Also, Black Tom isn't Juggernaut's buddy anymore? When?
i seem to remember in on of the fights between juggernaught and colososus seemed to be in a bar, whats so special about this random comment is that by coloosus spilling drinks over juggernaught it caused him to fight, if this hadnt have happerned he would have fallen pray to selene aka the black queen who was flirting with him realy badly and he was been a sucker for it ( as the black queen was going to drain his life energy)
my point is that sexual polotics can play a part in swaying the juggernaught.
all she has to do is use her special skill of running away to great effect. or alternative she could randomly form a brootherhood out of nowhere to help her fight..... woooo mimic.....( oh no not again!!)