The different forms of the deities have been revealed to the rishis who have composed the dhyana-mantras.As Swami Nigamananda writes
The formless brahman assumes form to shower grace on the devotee (Tantrik-Guru,Sarasvata Math, page 56).
Its also said :'Sadhakaanaam hitaarthaya brahmano rupakalpana' : For the benefit of the aspirants, Brahman assumes forms.
So why One holds it and other does not ---this question has no answer in the scriptures. Some prefer to explain these symbolically, but thats upto them.
The same about the benefit.The dhyana is a part of puja.(Reference: Sastramulak Bharatiya Saktisadhana,Upendrakumar Das,RMIC, Vol 1, page 923).Any puja can be sakama, that is for gaining sme material thing or for attaining one of the eight siddhis (Ashta-Siddhi) or five types of Mukti(Panchavidha Mukti)or Moksha(Merging with Brahman). Worship can also be out of pure devotion or a way of getting pure devotion.That has to be mentioned while uttering the sankalpa-mantra as per the puja-vidhi. Devi is 'Chaturvarga-falapradaa' meaning She can bestow Dharma, Artha, Kaama and Moksha (Upendrakumar, page 335). A dhyana-Mantra of Bhavani reads
arunaam karunaataramgitaakshim dhrita-paasha-ankusha-mukhyachaapa-hastam/Animaadibhir aavritam mayukhair ahamiti eve vibhavaye Bhavanim//
meaning: I mediate on Mother Bhavani, who is red-coloured, eyes full of grace, holding paasa and ankusha, dhanur and vaana in four hands and is sorrounded by eight siddhis like Anima etc.
According to Tantra, Paasa are of eight types that binds a jiva and so Devi by Her grace can remove these paasha.According to the Kularnava-Tantra (13/30-31), the eight 'paasa' are
Ghrina,Lajjaa,Bhaya, Shanka, Jugupsa,Kula, Shila and Jaati.
ghrina shanka bhayam lajja jugupsa cheti panchami/ kulam silam cha maanam cha astau pashah prakirtitah//
iti ashtapaashah kevalam vandhanarupa rajjavah/
etair vaddhah pashuh prokto mukta etaih sadashivah// (Vairava-yamala)
Paasa also is used to mean Moha-paasha(bondage of Attachment) or Maya-pasha(bondage of worldliness).Devi is known as Mahamaya Who binds the jeevas by Her noose. And being pleased by worship, grants boon and frees from Her noose (Reference: Sri Sri Chandi, chapter 1, mantras 53-56).
Ankusha is the instrument to control an elephant. In our scriptures, mind is compared to a mad-elephent (matta kari) as Sri Ramakrishna refers to in His Kathamrita(Udbodhan, page 246,22 July 1883), which can be controlled by Devi with Her Ankusha.
But I repeat, Devi appears physically to the saints and so She has form, as mentioned in Kenopanishad (Uma Haimavati).