For simultaneous work from two computers, a shared or server-based system is safer than a standalone organizer.

From the suggestions given, you have three practical approaches:

1. Cloud storage + catalog software: Store photos in a synced service such as Dropbox, then manage them with software like Lightroom. This may work, but concurrent use can be tricky and wasn’t confirmed by the respondents.

2. Cloud-based photo management: A service like SmugMug lets you organize online with keywords, captions, galleries, and collections, and allows simple edits like cropping. This is a good fit if your priority is organization over advanced editing.

3. Multi-user photo management software: A dedicated server-based tool such as Daminion Server was specifically suggested for multi-user environments. This is likely the best match if two people need to tag and organize the same library at the same time.

In general, be cautious with single-user desktop organizers like Picasa in a multi-user setup, because simultaneous changes can cause conflicts or even library/content problems. Also, prefer workflows that store keywords/captions in standard metadata where possible, so your organization is less tied to one program.