This is fairly similar to a question I had answered here:
Which exercise program is better for fat loss?
To start, keep in mind (as another user had answered in the linked question) your diet is your key factor. So regardless of your choice, it is how and what you eat that will determine your results.
As someone who is already fit and wants to add muscles, home training might not be right for you or your goals. Home training is good for resistance and bodyweight style training, while it can be lacking the tools needed to properly break down the muscles needed for muscle growth and not just fat loss.
For muscle growth, what you want to do is relatively heavy sets of 8-12 reps for hypertrophy, essentially breaking down your muscle so that they rebuild and grow.
With this in mind, here is a little pro's list to compare your two options:
PROS FOR HOME
- Cost effective (in terms of monthly fees, but not so much for equipment you may need)
- Efficient (you can train when you want to, without displacing yourself)
- Privacy, meaning you avoid any negative feelings such as nervousness or embarrassment when starting out
- Comfort. You are home, so you can train, shower, dress, etc. however you feel fit without worrying about others and your surroundings.
PROS FOR THE GYM
- Plenty of different machines and weights you might not be able to afford for home use. Also means if you go up in weight you do not need to go buy a brand new set of dumbbells for just a 5 pound increase, or even worse, always stay at the same weight.
The atmosphere is great, as there are plenty of people who are there to help guide you in the right direction, provide motivation, and answer questions when you have them.
Spotter's are available. This means that when your goal is to push your limits and go heavy, you can ask a fellow gym patron to spot you to keep you safe. Something you cannot do at home, and you do not want to take the risk of pushing too far to your limits when you are without a spot.
As someone who started out with home training and then migrated to a gym, I would really say if you want real results you should go to the gym. Just make sure you give nutrition the importance it needs, and you will see results.