Brightness and contrast ratio, inversely proportional? I'm comparing the features of 2 projectors, which are very similar between them. They both have 1300 lumens.

However I was surprised to see the following values:

Projector 1
Brightness (lm) 3000
Contrast ratio 2000:1

Projector 2
Brightness (lm)*1*2 1300 (Max)
Contrast ratio*1  3600:1

What does this mean ? They are both for home videos, but is the second one more suitable to darker environments, because it has less brightness ? But it offers better color quality, with more contrast ? Is this analysis correct ?

Also, not sure what "*1*2" means, and why they wrote (max). Probably it provides less brightness on average.
On that particular specification page the *1 and *2 mean look further down the page at notes 1 and 2, which are as follows:

*1: Varies depending on conditions

*2: All brand names and product names are trademarks, registered trademarks or trade names of their respective holders. Lamp life specification is an estimate based on verification under proper conditions and is not the duration of the warranty. Lamp will shut-off automatically when usage reaches the specified estimated maximum lamp hours. Service life may vary widely depending on usage and operating environment and conditions, as well as users' adherence to the maintenance and cleaning procedures provided in the user manual.

In terms of which one is best - it will depend on your needs, but the second one has higher frame rate and better contrast, which for most applications will be what you need, however if you do need the extra brightness for displaying in brighter environments, the first one may be more appropriate for you.