Will I increase my strength by doing 100 reps of bicep curls? Or will 15 reps of heavier weight be better?
It depends on the weight.
Doing 15 reps of 5 pounds and you can still do 85 more reps without being tired, then doing just 15 reps would be pointless.
The ideal rep range is to optimally increase strength is generally 1–4 reps. Most people will do 8–12 reps and have great results, though. That said, the key thing to note isn't how many reps you're doing. It's the fact that you can only do that many reps with the amount of weight you're lifting.
The fact that you've done 15 or 100 reps doesn't matter as much as the fact that you've worked the muscle to near exhaustion. You can gain strength with 100 reps, but it's usually through diminishing returns. By exhausting your type I muscles with the first 90 reps, your type II muscles will take over for the last few reps and you should be exhausted afterwards.
It's not an ideal way of building muscle because it takes a ton of time to do all those reps and your type I muscles will grab the rebuilding resources to fix itself at the cost of your type II muscles making strength growth slower.
If you can, lift the heaviest weight you can to be able to do 8–12 reps.
If you can't, you can modulate your exercise with lighter weight by doing it faster, more explosively (with excellent form) and doing more reps.