The basics of 4e

[heffroncm]

Also, what most people overlook in their adherance to +1 = 5% is that Attack bonuses and penalties are purely relative.  If you are facing an enemy which you must roll a nat16 to hit, that -1 causes you to miss 20% more frequently.  Even on a low defense opponent that you only need a nat11 to hit, a -1 removes 10% of your hits.  A longsword brings about 20% less average damage per W of the power, which is significant, but most powers have more effects on a hit than pure damage.

[phelanarcetus]

This would actually depend on the AC which you are facing.  1d10 is more damage than 1d8, granted.  The question is whether (5.5 + stat) x (chance to hit) > (4.5 + stat) x (chance to hit + 0.05).
Given a +4 Str, and ignoring crits for simplicity, this tells me that if you have a 45% or better chance of hitting with the axe, you are better off.  When your hit chance is less, the longsword's extra proficiency bonus is superior.

That also doesn't take into account having Dwarven Weapon Training available but not having Eladrin Solider available, for example, or anything about particular available weapon properties, or later feats.

I presume being able to target multiple defenses is valuable.  Fighters are in bad shape here; they have four attacks which are not against AC; all of those are against reflex.  Assuming you want to stick to Strength vs. X, Cleric is the best multiclass option, as Cleric provides vs. Fort and vs. Will attacks; Paladin only gives vs. Fort from a paragon path, Warlord has very few, and ranger has exactly one Strength vs. not-AC.  Your next best bet as a fighter would be to seek out Con-using Warlock powers.