Personally I like using both. Barbells and BW stuff both have their place. Dumbbells, machines and bands too. Even rings and bars can be great. It's not so much about the tool as it is using it well, smart and having a certain goal in mind.
The rep and set scheme also varies. 5x5 is alright, but you can do it however you want and in regards to what you want to achieve.
Personally I think that practicing and getting good at a squat and a deadlift variation (without chasing numbers) is great for your lower body strength, injury prevention and overall body mechanics. It's about getting good at the movements and progressively loading over time, then the strength will come. Add to that some single leg work like single leg lunges and single leg deadlift variations with dumbbells and you get some great balance, stability and athletic benefits. Pistols are also great, but requires a mobility that might take some time to build up to. Using a few assistance exercises like leg curls or GHR helps prevent especially knee injuries as well. Band pulls for healthy shoulders and progressive BW work for your upperbody. Perhaps some controlled dumbbell rows and OHP pressed with a barbell. That could be the meat of your exercise program.
What it really comes down to, no matter what, is a smart program with focus on form and a balanced program that targets bad habits and weak spots. I view this as something supplementary to your sport. Meaning you build your strength base slowly and focus on steady reps with a controlled eccentric. Build that base so that you are not only stronger, but less injury prone.
Then over time you can implement the power stuff like velocity training with barbells, plyos, med ball, hammers, power cleans, CMJ jump, agility drills, banded power punches, knees and kicks, and generally start working more explosive components.
The really juicy stuff is sport specific work, but that takes someone who knows what they are doing. First things first.