A feature of the D&D3 rules is that a level gained is not linear. That is, going from 12th to 13th level in a class generally gets you more than going from 2nd to 3rd level. However, it can be tricky to understand just what each level gets you.
Going up from level N to the next level requires collecting Nx1000 experience. You then get a fixed bonus to attack, hit points, and saves which is evenly distributed among levels. However, there are other non-linear benefits: including multiple attacks, progressive feats, and spells. As an example, below I show a table of the maximum healing for a cleric per day for levels 1 through 8. This assumes a cleric with Wisdom 16 or 17, whose domain spells cannot be used for healing.
| Cleric Max Healing per Day (assume Wis 16) | |||
|---|---|---|---|
| 1 | 4+2x(d8+1) | = 15hp | (---) |
| 2 | 4+3x(d8+2) | = 22.5 | (+7.5) |
| 3 | 4+3x(d8+3)+2x(2d8+3) | = 50.5 | (+28) |
| 4 | 5+4x(d8+4)+3x(2d8+4) | = 78 | +27.5 |
| 5 | 5+4x(d8+5)+3x(2d8+5)+2x(3d8+5) | = 122 | (+44) |
| 6 | 5+4x(d8+5)+4x(2d8+6)+3x(3d8+6) | = 161.5 | (+39.5) |
| 7 | 6+5x(d8+5)+4x(2d8+7)+3x(3d8+7)+1x(4d8+7) | = 204 | x(+42.5) |
| 8 | 6+5x(d8+5)+4x(2d8+8)+4x(3d8+8)+2x(4d8+8) | = 259.5 | (+55.5) |
This nonlinearity is particularly important for multiclassing. Since the level benefits of classes are non-linear, when you get a new level you gain more by raising your highest-level class rather than raising a lower-level class. Thus, even if you ignore the potential XP penalties, multiclassing is discouraged.
In AD&D2, the level costs were exponential until level 9-12, and then switched to linear. That is, the XP required for level 3 might be twice that of level 2, but after level 10 only a fixed number is needed for each level. The non-linearity of level gains was similar, however, at least for spellcasters.
This difference has important consequences for multiclassing. In AD&D2, you split your XP's between your classes and calculated each level separately. Because of the exponential cost of levels, an AD&D2 multiclass character only lagged 1 to 3 levels behind single-class characters until level costs became linear. i.e. For the same XP as a 12th level fighter, you might have a 10/11 fighter/wizard. In D&D3, the same XP as a 12th level fighter will only get you a 6/6 fighter/wizard.
The AD&D2 multiclass averaged hit points and takes only the best attack bonus (i.e. average of 10d10 and 11d4 and the fighter attack bonus). In D&D3, you add together the hit points and attack bonuses of all classes (i.e. 6d10+6d4 hit points and attack bonus of a 9th level fighter). The D&D3 multiclass has slightly better hit points than the AD&D2 multiclass, but its spellcasting ability is pitiful and you miss out on many extra abilities of high level.
The following table shows what spells are gained at what level: i.e. what spells you gain upon reaching a level, rather than the total of all the spells you have thus far. This is useful is seeing how each level gain progressively gets you more per level.
To interpret this, you need some estimate of how much a higher-level spell is worth. I would say that the value of a spell is slightly more than linear with level. i.e. A 2nd level spell is worth more than two times a 1st level spell. For simplicity, though, I think that assuming linear worth is close enough for most purposes.
Cleric/Druid/ : Sorcerer : Bard : Paladin/
Wizard : : : Ranger
0 1 2 3 4 5 6 7 8 9 : 0 1 2 3 4 5 6 7 8 9 : 0 1 2 3 4 5 6 : 0 1 2 3
=====================================================================
1 : 3 1 - - - - - - - - : 5 3 - - - - - - - - : 2 - - - - - - : - - - -
2 : 1 1 - - - - - - - - : 1 1 - - - - - - - - : 1 0 - - - - - : - - - -
3 : - - 1 - - - - - - - : - 1 - - - - - - - - : - 1 - - - - - : - - - -
4 : 1 1 1 - - - - - - - : - 1 3 - - - - - - - : - 1 0 - - - - : 0 - - -
5 : - - - 1 - - - - - - : - - 1 - - - - - - - : - 1 1 - - - - : - - - -
6 : - - 1 1 - - - - - - : - - 1 3 - - - - - - : - - 1 - - - - : 1 - - -
7 : 1 1 - - 1 - - - - - : - - 1 1 - - - - - - : - - - 0 - - - : - - - -
8 : - - - 1 1 - - - - - : - - - 1 3 - - - - - : - - 1 1 - - - : - 0 - -
9 : - - 1 - - 1 - - - - : - - - 1 1 - - - - - : - - - 1 - - - : - - - -
10 : - - - - 1 1 - - - - : - - - - 1 3 - - - - : - - - - 0 - - : - 1 - -
11 : - - - 1 - - 1 - - - : - - - - 1 1 - - - - : - - - 1 1 - - : - - 0 -
12 : - - - - - 1 1 - - - : - - - - - 1 3 - - - : - - - - 1 - - : - - 1 -
13 : - - - - 1 - - 1 - - : - - - - - 1 1 - - - : - - - - - 0 - : - - - -
14 : - - - - - - 1 1 - - : - - - - - - 1 3 - - : 1 - - - 1 1 - : 1 - - 0
15 : - - - - - 1 - - 1 - : - - - - - - 1 1 - - : - 1 - - - 1 - : - - - 1
16 : - - - - - - - 1 1 - : - - - - - - - 1 3 - : - - 1 - - - 0 : - 1 - -
17 : - - - - - - 1 - - 1 : - - - - - - - 1 1 - : - - - 1 - 1 1 : - - 1 -
18 : - - - - - - - - 1 1 : - - - - - - - - 1 3 : - - - - 1 - 1 : 1 - - -
19 : - - - - - - - 1 - 1 : - - - - - - - - 1 1 : - - - - - 1 1 : - 1 1 1
20 : - - - - - - - - 1 1 : - - - - - - - - - 2 : - - - - - - 1 : - - - 1
=====================================================================
0 1 2 3 4 5 6 7 8 9 : 0 1 2 3 4 5 6 7 8 9 : 0 1 2 3 4 5 6 : 0 1 2 3