I couldn't see a big difference between the two accounts' preferences so the problem must be somewhere else.
Here's the report. I will appreciate very much any comments, conclusions, guess..
EtreCheck version: 5.3 (5031)
Report generated: 2019-07-03 07:25:37
Download EtreCheck from https://etrecheck.com
Runtime: 4:30
Performance: Good
Sandbox: Enabled
Full drive access: Disabled
Problem: Apps are crashing
Description: 
Safari shuts down unexpectedly.
Major Issues:
    Anything that appears on this list needs immediate attention. 
    No Time Machine backup - Time Machine backup not found.
    Obsolete hardware - This machine may be considered obsolete.
Minor Issues:
    These issues do not need immediate attention but they may indicate future problems or opportunities for improvement. 
    Upgradeable hard drive - This machine’s hard drive could be replaced with an SSD. This would dramatically improve your machine’s performance.
    Upgradeable RAM - This machine has upgradeable RAM that would help its performance.
    Limited drive access - More information may be available with Full Drive Access.
Hardware Information:
    MacBook Pro (15-inch, Mid 2010) - Obsolete!
    MacBook Pro Model: MacBookPro6,2
    1 2,4 GHz Intel Core i5 (i5) CPU: 2-core
    4 GB RAM - Upgradeable
        BANK 0/DIMM0 - 2 GB DDR3 1067 ok
        BANK 1/DIMM0 - 2 GB DDR3 1067 ok
    Battery: Health = Normal - Cycle count = 583
Video Information:
    Intel HD Graphics - VRAM: 288 MB
        Color LCD 1440 x 900
    NVIDIA GeForce GT 330M - VRAM: 256 MB
Drives:
    disk0 - ST9320325ASG 320.07 GB (Mechanical - 5400 RPM)
    Internal SATA 1.5 Gigabit Serial ATA
        disk0s1 - EFI (MS-DOS FAT32) [EFI] 210 MB
        disk0s2 [Core Storage Container] 319.08 GB
            disk1 - Macintosh HD (Journaled HFS+) 318.71 GB (31.38 GB used)
        disk0s3 - Recovery HD [Recovery] 650 MB
Mounted Volumes:
    disk1 - Macintosh HD
        318.71 GB (31.38 GB used - 287.07 GB free)
        Journaled HFS+
        Mount point: /
Network:
    Interface Bluetooth-Modem: Bluetooth DUN
    Interface en0: Ethernet
    Interface fw0: FireWire
    Interface en1: Wi-Fi
        802.11 a/b/g/n
    Interface en2: Bluetooth PAN
System Software:
    macOS High Sierra 10.13.6 (17G7024) 
    Time since boot: Less than an hour
Notifications:
    Notifications not available without Full Drive Access.
Security:
    Gatekeeper: Enabled
    System Integrity Protection: Enabled
System Launch Agents:
    [Not Loaded] 17 Apple tasks
    [Loaded] 178 Apple tasks
    [Running] 99 Apple tasks
System Launch Daemons:
    [Not Loaded] 38 Apple tasks
    [Loaded] 196 Apple tasks
    [Running] 102 Apple tasks
Launch Agents:
    [Other] com.adobe.ARMDCHelper.cc24aef4a1b90ed56a725c38014c95072f92651fb65e1bf9c8e43c37a23d420d.plist (Adobe Systems, Inc. - installed 2019-03-29)
Launch Daemons:
    [Loaded] com.adobe.ARMDC.Communicator.plist (Adobe Systems, Inc. - installed 2019-03-29)
    [Loaded] com.adobe.ARMDC.SMJobBlessHelper.plist (Adobe Systems, Inc. - installed 2019-03-29)
    [Loaded] com.adobe.fpsaud.plist (Adobe Systems, Inc. - installed 2019-05-27)
User Login Items:
    iTunesHelper.app (Apple - installed 2019-04-14)
        (Application - /Applications/iTunes.app/Contents/MacOS/iTunesHelper.app)
Internet Plug-ins:
    AdobePDFViewerNPAPI: 17.012.20098 (Adobe Systems, Inc. - installed 2019-05-17)
    FlashPlayer-10.6: 32.0.0.207 (Adobe Systems, Inc. - installed 2019-06-27)
    Flash Player: 32.0.0.207 (Adobe Systems, Inc. - installed 2019-06-27)
    AdobePDFViewer: 19.012.20034 (Adobe Systems, Inc. - installed 2019-05-17)
Audio Plug-ins:
    BluetoothAudioPlugIn: 6.0.7 (Apple - installed 2019-05-28)
    iSightAudio: 7.7.3 (Apple - installed 2019-05-28)
    AirPlay: 2.0 (Apple - installed 2019-05-28)
    AppleAVBAudio: 683.1 (Apple - installed 2019-05-28)
    BridgeAudioSP: 4.69.2 (Apple - installed 2019-05-28)
    AppleTimeSyncAudioClock: 1.0 (Apple - installed 2019-05-28)
3rd Party Preference Panes:
    Flash Player (installed 2019-05-27)