Does GLaDOS hate Atlas, the blue robot?

Solution 1:

GlaDOS seems more interested in dividing Blue and Orange than picking favorites, and will show favor to either Blue or Orange. In the Yogscast, GlaDOS awards Orange "five science collaboration points" in one level (10:27 in), then awards the same to Blue in a later level (11:45 in):

In a later episode, GLaDOS states that:

the challenge would present a challenge for one of the two given one's performance so far, but doesn't say who (0:00)
the two form an excellent partnership with one handling the cerebral challenges and the other "ready to ponderously wander into action should the test suddenly become an eating contest", again doesn't say who is better (5:28)

But the smoking gun, as it were, that she doesn't necessarily favor Orange comes at 9:00 when she states:

To reiterate, this is not a competition. Still, if it were, Blue would be winning. [inaudible] Blue receives five science collaboration points.

So whether it's dependent on performance is possible (although unlikely if you watch these videos), but she doesn't seem to have a complete disdain for Blue.

Solution 2:

The responses may not always be used with the same frequency, but most of her taunts to one seems to have an equal and opposite. That said, she does flat out say she hates blue a little more, one remark I can't find the dual of.

Counting up though:

for blue, 7 "compliments", 22 denigrations = -15
and orange, 7 "compliments", 18 denigrations = -11

So also going by the numbers, it does seem like she hates blue a little more.

Anti-Blue

glados.anti_taunt16 "For that Blue is penalized fifty science collaboration points."
glados.anti_taunt20 "Fine, 500 point penalty for Blue."
glados.botcoop_competition13 "I don't want to drive a wedge between the two of you, but I've been studying Blue's performance, and I don't know how to put this... I'm certain you're trying very hard."
glados.coop_scoring01 "Blue is penalized"
glados.coop_test_chamber_orange03 "It would be pointless for either of us to hurt Blue’s feelings. But it’s clear to everyone monitoring the test who’s carrying who here."
glados.coop_test_chamber_both12 "As an impartial collaboration facilitator, it would be unfair of me to name my favorite member of your team. However, it’s perfectly fair to hint at it in a way that my least favorite member probably isn't smart enough to understand. Rhymeswithglue. Orange you are doing very well."
glados.mp_coop_laser_209 "For instance, Blue, you just lost two opportunity advisement points."
glados.mp_coop_laser_crushercrush04 "Blue, orange isn't a human. The lesson on trust only needs to be taught once. Blue is penalized 1 science collaboration point."
glados.mp_coop_rat_mazedeath01 "Clearly that was blue's fault. Blue is penalized 3 science collaboration points."
glados.mp_subterfuge03 "Yes Orange, we are alone. Blue can't hear you."
glados.mp_subterfuge21 "Orange, I agree. I never noticed that about Blue before."
glados.mp_subterfuge23 "Blue, Orange and I were just discussing your behavior on the last few tests."
glados.mp_subterfuge24 "I have to agree. Blue is penalized 75 science collaboration points."
glados.mp_subterfuge45 "If Orange had said those things about me, Orange would never make it to the next reassembly station."
glados.mp_subterfuge_misc06 "I just hate Blue a little more."
glados.mp_subterfuge_misc14 "Blue, please disregard the following statement: Orange, you have been a shining light in an otherwise ungodly morass of incompetence."
glados.mp_subterfugedeath_blue01 "You were right, Orange. Blue was dumb enough to fall for your trap."
glados.mp_subterfugedeath_blue02 "Orange, that transpired just as you said it would."
glados.mp_subterfugedeath_blue03 "I agree, Orange. That was entertaining."
glados.mp_subterfugedeath_blue04 "Yes Orange, Blue did act like a fool just now."
glados.mp_subterfugedeath_orange06 "Yes, I know you did that, Blue. Don't look so proud."
glados.mp_subterfugedeath_orange08 "Blue, being the last one standing is not the goal."

"Pro"-Blue

glados.botcoop_competition03 "Still, if it were, Blue would be winning."
glados.coop_get_gun11 "Blue is awarded five points!"
glados.coop_vault_interruption09 "The portal will open and something will happen that Subject Blue is too smart to need any instructions about in three. Two. One."
glados.mp_coop_come_alongstart04 "Blue, you are very good at being an example."
glados.mp_coop_laser_crushercrush02 "Blue just taught orange a valuable lesson in trust. For that, blue receives 14 science collaboration points."
glados.mp_coop_laser_crushercrush06 "Blue, now you're just being cruel. Blue receives 25 science collaboration points."
glados.mp_coop_rat_mazedeath02 + glados.mp_coop_rat_mazedeath03 "Blue! Orange has always been my favorite." "Until now."

Anti-Orange

glados.anti_taunt17 "For that Orange is penalized fifty science collaboration points."
glados.anti_taunt21 "Fine, 500 point penalty for Orange."
glados.coop_scoring02 "Orange is penalized"
glados.coop_test_chamber_blue03 "I’ve been listening to Orange talk and I don’t know how you put up with it, I really don’t. You have the patience of a saint."
glados.coop_test_chamber_blue06 "I can’t keep quiet about this. I think Orange is actively trying to sabotage your success. Let’s keep this between us."
glados.coop_test_chamber_orange06 "I’m shocked you’d say that, Blue. If you killed your partner the test—I’m sorry. Wrong feed. Carry on, Orange. Good work.`
glados.mp_coop_come_alongstart02 "Orange, can you write down all the ways you feel unworthy, ashamed, or inferior?"
glados.mp_coop_laser_210 "clr:163,193,173For instance, Orange, you just lost two opportunity advisement points."
glados.mp_coop_laser_crushercrush03 "Orange, blue isn't a human. The lesson on trust only needs to be taught once. Orange is penalized 1 science collaboration point."
glados.mp_hubreturn11 "Blue, I wouldn't have trusted Orange in that course either."
glados.mp_subterfuge07 "Correct Blue, Orange can't hear you."
glados.mp_subterfuge22 "Blue, I agree. I never noticed that about Orange before."
glados.mp_subterfuge25 "Orange, Blue and I were just discussing your behavior on the last few tests."
glados.mp_subterfuge26 "I have to agree. Orange is penalized 75 science collaboration points."
glados.mp_subterfuge47 "If Blue had said those things about me, Blue would never make it to the next reassembly station."
glados.mp_subterfuge_misc07 "I've been doing some reading. Did you know that the word orange is derived from the same Latin root as the word traitor?"
glados.mp_subterfugedeath_orange02 "Blue, that transpired just as you said it would."
glados.mp_subterfugedeath_orange03 "I agree, Blue. That was entertaining."

"Pro"-Orange

glados.botcoop_competition04 "Still, if it were, Orange would be winning."
glados.coop_get_gun10 "Orange is awarded five points!"
glados.coop_vault_interruption08 "The portal will open and something will happen that Subject Orange is too smart to need any instructions about in three. Two. One."
glados.mp_coop_come_alongstart03 "On second thought we don't have the time, just look at how much better you are than blue."
glados.mp_coop_laser_crushercrush01 "Orange just taught blue a valuable lesson in trust. For that, orange receives 17 science collaboration points."
glados.mp_coop_laser_crushercrush05 "Orange, now you're just being cruel. Orange receives 25 science collaboration points."
glados.mp_coop_rat_mazedeath02 "Blue! Orange has always been my favorite."

(Anti-one vs. pro-other is a bit arbitrary...)

There are also plenty of general jabs that don't really seem to favor either side, but are just (vain) attempts to develop mutual animosity between the partners.