So, for the past days I've been looking online for all kinds of headphones and I wanted help deciding between the Beyerdynamic Custom One Pro Plus and the Sony's MDR-1A because of their reviews and they're both at the same price. I wanted ones that have good bass, but not too much and that a could use them at home in my pc and also on my phone when I get out.

The COPs are great headphones and their variable bass makes them well-suitable for indoor and outdoor use as low frequencies usually tend to drown in the ambient noise outside. However, thay are quite large and heavy compared to the MDR-1A.
 
The MDR-1A are very good sounding, light headphones, very comfortable and well built despite their light weight. The main downside for me is the bass. It's not very detailed and a bit loose. It didn't bother me when I didn't know better, but compared to the COPs, it's a step down. The mids and highs are very good though and overall it's the more balanced sound signature.
 
So if you want comfortable, more portable headphones, get the MDR-1A. If you want a more versatile sound, and can give in on comfort and portability, get the COPs.

Thank's for the feedback, but do you think the better bass is worth it instead of the better mids and highs?

I think it will come down to personal preference. It would be best if you could hear both  before purchasing, but I know that can be difficult in some cases.
 
For me personally the COPs are too large for on the go, so I would go for the MDR-1A. However, I have seen other people wearing large headphones without concerns. It again depends on your personal preference.
 
As far as sound goes, I think the versatility of the COPs make them overall the better choice for you.