Have I missed something, or is Strength really only worth it when it is the only option?
Let's say you want to hit someone in close combat, no matter the weapon. Each die has 50% probability to grant you a success when rolling for damage and 10% to lose one success, so 0.4 successes on average. That's all that Strength dice do: providing you with 0.4 average health level of damage per die, given that you have already hit successfully.
Dexterity is used when you roll to hit, with the same 0.4 average successes per die. But if you roll more successes than needed, they are added as damage dice too! So by increasing Dexterity, not only do you increase your damage, but also your chances to successfully hit. For example, with Dexterity 2 you roll 0/1/2 successes with a chance of 35%/40%/25% respectively, and with Dexterity 3 chances of 0/1/2/3 successes are 26%/31.5%/30%/12.5% (against standard difficulty of 6).
This is especially important when your enemy performs a defensive maneuver (parry, block, dodge).
The only case when you probably want to look for more damage is when difficulty to hit increases, such as if your enemy uses a shield. If the difficulty to hit is 7, each Dexterity die only gives 0.3 successes on average, while each Strengh die still gives 0.4.
But even then Strength is not the best solution! Go for Potence: it gives you automatic successes on all Strength-related rolls (even though you need to spend blood points for it in V20 edition). It is a plain +1 success per level. Yes, Potence is a bit more expensive — at character generation it costs 7 freebie points, and attributes cost 5 — but it gives exactly 2.5 times more damage for that, and is far more stable! Plus sometimes, when you don't feel that you need to spend blood, you can just go with the Strength bonus alone. For XP, Potence cost equals current rating × 5 if it is in-clan Discipline, or ×7 if out-of-clan, and Strength cost is always current rating × 4. The only moment when you should buy Strength as a neonate to get more successes on damage rolls on average is when your Strength costs less than (cost of Potence × 2.5). If Potence is an out-of-clan Discipline, this only happens when Potence is on level 4 and Strength is on level 1$ if the latter is on level 2, on Potence level 4 if you buy Strength, you buy the same average amount of successes per attack with less stability.
OK, let's say Potence is already at level 5, so is Dexterity, and you can't increase it further. Then Celerity is the answer: each level effectively gives you the ability to attack more times per turn.