Here are a few good reasons to go with Mapme as opposed to Google My Maps.

Product Mapme Google My Maps
Place Tags Yes No
Feed Yes No
Events Feature Yes No
Jobs Feature Yes No
Alerts Yes No
Email Popup Yes No
Branding Yes No
Map Views Yes No
Reports Yes No
Custom Call To Action Yes No
Custom URL Yes No
Claim System Yes No
Star Ratings Yes Partially
Reviews Yes Partially
Community Crowdsourcing Yes Partially