The imposter slid. I have to address the points made by <PERSON> his answer.
1. As <PERSON> himself remarked the intention was that the imposter slid. He also states that this idea did not make it to the screen. By that however is (most likely) meant that it was never revealed on screen that the imposter slid. It was clearly intended that such a reveal should have taken place at some point in the future.
2. The episode Dino Veritas does not provide sufficient evidence to conclude that the correct Professor slid. First of all, the imposter is very smart. He knows in the very moment that the Sliders arrive in the world of truth collars that he has to think on his feet in order to trick the lie detector. If the collar works in any way similar to the lie detectors that we know, then this is not too difficult for him. He has only to be convinced by the truth of what he is saying in order for his heart rate and vital signs not to indicate to the device that he is lying. Even if there is some kind of AI technology parsing the sentences uttered, it can still be tricked by sentence disambiguation issues. Of course the sliders could have asked him a straight, direct question regarding this matter. But this at least is never shown on screen, therefore we should not assume they did. What is shown however, is them meeting up for the slide. This implies that the imposter had some alone-time to figure out all the quirks of the truth collars and prepare himself. The following statements in question can thus be explained easily:
(1) On our earth, man and dinosaur lived millions of years apart. [To <PERSON>.]
(2) In the world where we come from, dinosaurs are long extinct, and this area here is the great city of San Francisco. [To the holographic scientist.]
(3) We have certainly seen the best and worst of each other. [To <PERSON>.]
(1): If the (EDP) Professor thinks at the moment of utterance of this statement that 'our earth' refers to the people that live on Earth Double Prime (including the Professor himself), then he can make the statement without triggering the collar. 663
Of course <PERSON>, and anyone listening, can interpret the sentence differently, i.e. such that the possessive pronoun 'our' refers to the earth of the Professor AND <PERSON>, but that is merely a possible interpretation. Earth Double Prime is so similar to Earth Prime, that part of the statement, that the dinosaurs are long extinct (on EDP), itself is clearly true.
(2): This is a true statement on the face of it. They all come from earth double prime. Sometime before landing on truth collar world, they indeed all came from EDP. They do not all 'originally stem from' EDP, but that is not the intended meaning of the sentence.
(3): Again a true statement. The Professor from EDP has read <PERSON>'s diary. So he indeed has 'seen' (in his mind, while reading the diary) the best and worst of the other sliders. On the other hand, the sliders have seen the worst of him on EDP (he stole the timer and tried to take all the credit for sliding etc.). They presumably also have seen the 'best' of this version of the Professor. He actually mutters to himself 'foolish old man' in this episode, indicating that he thinks rather lowly of himself. So perhaps he thinks the way he is acting now is probably the best they have seen of him. Altogether, the statement is the TRUTH, also if the EDP Professor utters it.
Come to think of it, (3) is a particularly curious statement to make, if this was the Professor from Earth Prime. It seems much more plausible for the EDP Professor to make such a statement. What is the worst they could possibly have seen of the Earth Prime Professor afterall? On the other hand the statement fits in well with the whole attitude of the Professor in this episode, somehow blaming himself for tripping over a rock ('foolish old man'). It is plausible that he is probably feeling remorse or at least regret for his deeds in Post Traumatic Slide Syndrome.
1. Other evidence for the Earth Double Prime Professor have already been stated in this thread. I think one of the most compelling is the football remark made in 'The Guardian', in an episode directed by <PERSON>, making it much more Canon that the wrong Professor slid than not in my view.
2. Taking the above disproof of <PERSON> answer, together with the positive evidence stated in 1. and 3., I think there is a slight surplus of evidence for the notion that indeed the imposter slid. In other words, the Professor is still alive and well on Earth Double Prime! 663