I have 2 real estate sites, A and B.

Site A produces an XML feed for real estate listings in Chicago.

Site B is a real estate site that shows listings in New York.

Is it elementary to create some code so that Site B (New York) grabs
the XML feed from Site A (Chicago), parses it, and combines the
Chicago listings with its own NY listings into one searchable,
sortable list on site B?  (no changes will be done to listings from
XML feed)

Also, I have the option to connect to the database remotely and run
SQL commands... is this method just as good?  Which is normally
preferred?

What else should I keep in mind to make this a smooth process?  The sites
are using php/mysql.

Thanks.

1) You could output XML files at both sites, combine them into one XML
file, and then use XPath to generate resultsets you need. 2) You could
set up replication between both databases and then use SQL to generate
resultsets you need. 3) You could query both databases at the same
time and combine resultsets.

It all depends on how exposed your data sources are. e.g. Can website
A access database for website B? Can website B access database for
website A?

SQL solutions tend to be more flexible and cost effective than
XML/XPath solutions. SQL skillset is more common than XML / XPath
among consultants.

MySQL access from PHP is very easy to implement. XML/XPath solution
from PHP will require someone with above-average scripting skills.