At least for CO2 emissions it looks like they're roughly on par with each other. Impossible Foods claims a 3.5 kg CO2-eqv. per kg product[1]. For chicken meat, the emissions depend a lot on how and where they're raised, but according to this UN report[2] it's roughly 2.7-8 with an average of ~5.4. It's a bit lower for eggs at 2-5 with an average of ~3.7.
EDIT: This study[3] has a more detailed breakdown which roughly matches the numbers from the UN report. For meat: 2.3-12, average 5.7, median 4.3. For eggs: 2.6-7.6, average 4.2, median 3.8
EDIT: This study[3] has a more detailed breakdown which roughly matches the numbers from the UN report. For meat: 2.3-12, average 5.7, median 4.3. For eggs: 2.6-7.6, average 4.2, median 3.8
[1] https://impossiblefoods.com/mission/lca-update-2019/
[2] http://www.fao.org/3/i3460e/i3460e.pdf
[3] https://science.sciencemag.org/content/360/6392/987