i am trying to make an assassin with either a fighter or ranger up to level 10. go
Are you looking for a dagger wielding assassin, a dagger and short sword, two short swords? It'll depend on what you really want out of the assassin and why aren't you also including rogue in the options as assassins are definitely very roguish with their ability to sneak attack and/or kill with a single strike from the shadows.
all pathfinder books are allowed and i am trying to keep as close to a full BAB as possible
Fighter 10/ Red Mantis Assassin 10
Ranger is the best way to go. Max out Human as your favored enemy, and do the same with Urban for your favored Terrain. Build him as a switch hitter as per treantmonk's guide because you want to be able to take down the target either in melee or at range.
Rangers have some nice spells for an assassin particularly Lead Blades and Gravity Bow. With Lead Blades you could be doing 2d6+21 points of damage and have a crit range of 15-20 with a Falchion vs a human at 10th level. That is assuming +6 to hit and damage for favored enemy, 18 STR, Power attack and improved Critical with the Falchion.
Rangers also have all the skills you will need as an assassin as class skills and a decent number of skill points. Fighter may give you more damage, but you will be hard pressed to get the skills, and abilities you need as an assassin. A nice bonus is that if you are in your favored terrain (Urban) you can't be tracked.
I agree that, of the two, Ranger is the better choice. But, the one fighter option that stands out for me is the Cad archetype in the Ultimate Combat book. It has a good range of skills and abilities that are certainly "rogueish". Good luck!