The best replacement for arcsde is arcgis server.

The best alternatives to arcsde are rated as following:
★★★★★  arcgis server
★★★★★  file geodatabase
★★  direct connect
★  oracle spatial

Your alternative for arcsde is not listed? Suggest!
Speaking about arcsde, one probably shouldn't forget about postgis.

Other search terms related to arcsde and their ratings are:
★★★★★ postgis
★★ oracle spatial
arcgis server
geoserver
You have in mind a companion for arcsde and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of arcsde in all years. Click on graph for more.
arcsde
arcgis server
file geodatabase