Which is more environment-friendly: LEGO bricks or Mega Bloks?
There are multiple ways to look at this question, but in any case, probably LEGO.
Production
LEGO has been prioritizing sustainability as of late, with all of their electrical uses and more already coming from sustainable sources.

Our sustainability mission
Our mission is to make all LEGO® bricks sustainably by 2030. Why? Because being sustainable is good for the planet! We want to make bricks out of things that we can grow again or are recycled. This is not easy as we want sustainable LEGO bricks to have the same high quality that you are used to, but what we know is this: big ideas may start small, but they will help us build a greener planet one brick at a time.
Reduce, Reuse, Recycle
At the LEGO Group, we want to play our part and make a positive impact on society and the planet, which our children will inherit, and it is this focus on future generations that drives our work. We believe we have a responsibility to minimise the environmental impact of our operations. However for us, minimising is not enough, we want to aim for zero environmental impact on the planet.
The LEGO Group aims to send zero waste to landfill by 2025, and in 2018 recycled 93% of all waste from our operations. Additionally, 100% of all plastic waste produced during the moulding of LEGO® bricks was recycled. This includes reusing some of the plastic resin in our own processes, as well as sending some of the waste to suppliers to be recycled and turned into other plastic products.
We’re big fans of wind power!
We’re proud of our achievement of being 100% balanced by renewable energy, due to the investments made in offshore wind farms in Germany and the UK by KIRKBI A/S – parent company of the LEGO Group. In 2018, the energy output from our investments in renewables was greater than the energy used at LEGO® factories, offices and stores.

I am not aware of nor was I able to find a similar effort being made by Mega Bloks, though I suppose it's possible they are doing it without advertising.
Disposal
As far as the environmental impact of the product when it reaches a landfill, it's a bit tougher to answer that question. It's unclear how different the  plastics the two companies uses is, and what the impact of those plastics is. The amount of plastic each company might use for a given piece might also differ. One thing I can say though is that LEGO is much more likely to be repurposed as it holds an after-market value much better.