The only place in fact where heirlooms are just amazing is around starting levels, and their power slowly wanes away.
I'm going to pick on the Bloodied Arcanite Ripper. Its a Two handed axe costing 3500 Justice Points or 95 Champion's Seals. Ill compare it with the sorts of weapons a 2-h warrior or paladin would be seeking to gain as they level up (in my opinion).
So, Level 1 BARipper
8.0 dps, 1 str, 2 sta, 1 crit
The Worn Battleaxe - Standard level 1 Warrior weapon.
Level 10 BARipper
13.0 dps, 4 str, 6 sta, 4 crit
Battleaxe of the Sober Dwarf (Alliance only)
7.2 dps 1 Str, +1 Sta
Level 11 BARipper
14.0 dps, 4 str, 6 sta, 4 crit
Arborcide Axe (Horde Only)
7.8 dps, 1 Str, 1 Sta
Level 18 BARipper
19.0 dps, 6 str, 9 sta, 6 crit
19.8 dps, 5 St, Chance on hit: Sends a shadowy bolt at the enemy causing 60 to 90 Shadow damage.
Level 24 BARipper
23.0 dps, 8 str, 12 sta, 8 crit
23.9 dps, 12 Str, 8 Sta
Level 35 BARipper
35.0 dps, 12 str, 18 sta, 12 crit
32.6 dps, 15 Str, 13 Sta
As you can see the blues range from just below to above the heirloom axe. Its lots and lots of points to buy one of these things so why not just use quest rewards and dungeon drops? Lazyness, you equip it and you can just level up. But if you spend a little bit fo time on gear you end up with a much better character. The disparity becomes severe when you reach 60.
((Note the weapon I'm using is avalible thought PvP. But its incredibly easy to get your hands on one. Ill do a post talking about it later.)
Level 60 BARipper
68.0 dps, 25 str, 38 sta, 25 crit
77.5 dps 26 Str, 41 Sta, 14 crit
It takes till level 65 for the Heirloom weapon to exceed the ability of the PvP weapon and then you get this quest axe...
Level 75 BA Ripper
78.0 dps, 29 str, 44 sta, 29 crit
81.6 dps, 31 Str, 30 Agi, 45 Sta
At 77 it equals it but you can pick up a Northrend green axe more often than not on the AH. 78 the Heirloom becomes useful again but just for two levels because at 70 you can get another pvp weapon.
Level 70 BA Ripper
124.0 dps, 47 str, 70 sta, 47 crit
140.4 dps, +66 Stamina, 19 hit, 50 crit, 14 haste, 100 Attp, 33 Resil
So the heirloom axe starts getting better and is almost there at 75 when another quest axe pops up.
Level 75 BARipper
138.0 dps, 56 str, 85 sta, 56 crit
145.3 dps, +61 Strength, +93 Stamina, 47 hit, 30 crit
The Bloodied doesn't catch up till almost at 77 and definetly at 78 but you can pick up a green Cataclysm weapon there and use it instead. The Heirloom axe stopping all stat advencement at 80.
This seems strange and wrong to me, the heirloom weapons used to be kings of leveling and only faced challenge from the blue quest weapons at 65 and 75. Now their constantly not the best weapon for you to use.