They both fall under Howard county government: so same police , fire, county exec, taxes etc.

Columbia you get the massive trail network and "tot lots" over most of the area. A lot of the properties are Columbia Association assessed, which is a few grand a year (tied to property value). Its technically an HOA, but you can have a second HOA if you buy a town house. The theory behind Columbia is that the yards are smaller, but you get more shared parks and open spaces. Schools range from great to below average. Redistricting happens every few years, so look at past maps before making assumptions.

Ellicott city is a straight up suburb for most of it. Bigger yards and houses. Sidewalk coverage is mixed. There are some larger county run playgrounds. Schools, for the most part are good in EC. Housing prices reflect this.

I would honestly look at both and Clarksville as well. Your budget is probably going to eliminate large chunks of the county.