One difference I have often heard said, is that a prayer is asking God respectfully whereas a spell is more about trying to influence events yourself.
That with Christianity a successful outcome is credited to God, but with Paganism it is the caster of the spell who is powerful.
I heard that the difference is that spells are credited to the caster.
A Christian prayer, as I see it, is the supplicant asking God to do something for them. A Witch's spell asks for a deity's help in achieving a goal, the witch using the powers of the natural world to achieve a result. There are few witches whim I know or know of, who consider themselves to be powerful enough to do this kind of thing on their own.
The old saying that God (or a Goddess) helps those who help themselves would seem to apply. The witch knows (or most of them do) know they are cannot do it alone, and are not too proud to ask for help.
Now this may not be true, and I don't see it always is, but some magic spells, by say a witch doctor does seem to be credited to him, rather than a deity.
A "witch-doctor" has nothing in common with a modern. or even the hsitorical, witch as witches operate.
Quoted from the Wikipedia topic "Witch-Doctor"
In its original meaning, witch doctors were emphatically not witches themselves, but rather people who had remedies to protect others against witchcraft. Witchcraft-induced conditions were their area of expertise, as described in this 1858 news report from England
Recourse was had by the girl's parents to a cunning man, named Burrell, residing at Copford, who has long borne the name of "The Wizard of the North:" but her case was of so peculiar a character as to baffle his skill to dissolve the spell, Application was next made to a witch doctor named Murrell, residing at Hadleigh, Essex, who undertook to effect a cure, giving a bottle of medication, for which he did not forget to charge 3s. 6d., and promising to pay a visit on Monday evening to the "old witch," Mrs. Mole, and put an end to her subtle arts... ... the news of the expected coming of the witch-doctor spread far and wide, and about eight o'clock there could not have been less than 200 people collected near the cottage of Mrs. Mole to witness the supernatural powers of the Hadleigh wizard.
Paganism is difficult to generalise about because it's so varied, but I'd be interested in your response Owlswing.
Do you think spells are more egotistical than prayers?
No.
Your OP says Witch/Pagan spell vs Christian prayer
It doesn't seem to include Pagan prayer 
unless you class a spell as a prayer.
I do, this is the point. They are both applications to a deity, for Christians, asking it to do something for them; for pagans, asking it to assist them to do someting for themselves.
