The other print on vinyl you mention is much less descriptive than the lambda print.. there are lots of "digital" printers.
With lambda, it's basically a combination of digital laser printing & the photographic process. I would give them the file at 300 dpi, regardless of what they asked for. The Lambda process can handle it. 100 DPI is probably their minimum. Also, they're talking about adhering the print to the perspex, which is a nice feature.
The others, with the vinyl print, will leave you with something that you have to adhere to the front of plexi (doing it to the reverse will be rather difficult. I don't really like vinyl prints.... I have one on my Defender, and I hat it every time I look at it. It was a bit cheaper, but I wish I had bought something a lot nicer.