Not the same God, unless you believe the God of Abraham sent a prophet to preach such things as:
"The city and everything in it is under the ban. Only Rahab the prostitute and all who are in the house with her are to live, because she hid the messengers we sent. * * * They observed the ban by putting to the sword all living creatures in the city: men and women, young and old, as well as oxen, sheep and donkeys."
That's from the OT.  God ordering everyone in Jericho be killed.  Sounds like the God of Abraham is every bit as bloodthirsty as Allah.