My experience - The only 2 PXAR I know is the 300 and Impala. Maxima is PCAR. I see the same rate issue from time to time, but it makes more sense to book LCAR as it gives the most flexibility at pick up.
LCAR - Haven't seen an ATS in a long time, but you'll probably see an CTS, XTS, or C300. You will probably get upgraded due to small LCAR options.