What are the philosphical differences between Gaudiya Sampradaya and Nimbarka Sampradaya? I know they both worship Radha-Krishna (unlike Pushtimarg where they worship Krishna as ShriNathji). What are the characteristics of these sampradayas which set them apart from each other?
Any discussion of philosophical differences between Vaiṣṇava sampradāyas should consider Vedānta darśana, and to do that properly would take many pages. So the quick summary:
Dvaitādvaita as defined by Śrī Nimbārka in his Vedānta-pārijāta-saurabha commentary (expanded by other commentators in his line) deals with the difference between Brahman, jīvātman (the individual soul) and jaḍa-prakṛti (dull matter) by saying essentially that the difference itself is real but Parabrahma Śrī Kṛṣṇa is free from the defects associated with ordinary souls and the material world. That's not a great synopsis but it's a complex topic, and I'm not nearly as familiar with dvaitādvaita as with the Gaudiya understanding.
Acintya-bhedābheda-tattva as defined by Śrī Baladeva Vidyābhūṣaṇa is accepted by Gaudiya Vaishnavas as replicating the lost explanations on Vedānta given by Śrī Caitanya Mahāprabhu to Sārvabhauma Bhaṭṭācārya. Although Gaudiyas primarily look to Śrīmad Bhāgavatam as the natural commentary on Vedānta, for an apples-to-apples comparison we can focus on the Govinda-bhāṣya commentary of Baladeva. Essentially, the starting point of acintya-bhedābheda-tattva is the sūtra śakti-śaktimator abhedaḥ (VS): there is no bheda (difference) between śakti (energy) and śaktimān (the wielder and possessor of energy). One of the core principles in Vedānta is reconciling the avikāratva (non-changing-ness) of Brahman with the ekatva (oneness) of jīvātman and Brahman. There are many statements of the Upanisads supporting both oneness (ekam evādvitīyaṁ brahma) and multiplicity (nityo nityānām), and the Gaudiya Vedānta perspective harmonizes these based on the ability of śakti to transform, while at the same time being accepted as non-different from Parabrahma Śrī Kṛṣṇa, who is sarva-śaktimān (the possessor and wielder of all energies). This approach is also known as śakti-parināma-vāda, the philosophy of transformation of the energetic aspect. Thus the acintya in acintya-bhedābheda-tattva refers to acintya-śakti, the various energies of Parabrahma Śrī Kṛṣṇa which are able to function independently as described in śaktir vividhaiva śrūyate and in viṣṇu-śaktiḥ parā proktā.
That is as much of a nutshell as I can manage on the topic of differences according to Vedānta.
There are many other differences in the areas of sādhana (devotional practice) and the concepts of sambandha (relationship with the worshipable deity), abhideya (functional relationship with the worshipable deity when the soul has escaped the bondage of matter) and prayojana (the ultimate goal). In Gaudiya Vaishnavism these are important topics differentiated by considerations of rasa, which is an entirely different topic.
The concept of worshipable deity (iṣṭa-deva or ārādhya) is also significant as Gaudiyas mostly worship Śrī Śrī Rādhā-Kṛṣṇa in the parakīya (unmarried) mood versus the svakīya (married) mood. But for Gaudiyas, the concept of rasa consideration (rasa-vicāra) is separate from consideration of Godhood (tattva) as stated by Śrīla Rūpa Goswami in his Bhakti-rasāmṛta-sindhu: siddhāntatas tv abhede 'pi śrīśa-kṛṣṇa-svarūpayoḥ - there is no difference according to tattva between Śrī Kṛṣṇa and the Lord of Vaikuṇṭha Śrī Nārāyaṇa (but such differences as exist are according to rasa).
The Gaudiya Sampradaya worships Sri Radha Govinda in parakiya (paramour) mood, in manjari bhava. The Nimbarka sampradaya worships Radha Krsna also but in swakiya (wedded) mood, in sakhi bhava. They have sambhoga rasa (union) and Sri Caitanya Mahaprabhu has vipralamba rasa (separation). In separation mood the gopis are remembering Krsna and having visions of Krsna and in these they experience the appearance of Krsna. So this is Vipralamba sadhana in line with the Srimad Bhagavatam.
Refer this link: http://www.bvmlu.org/contemporary/witdbngs.htm#:~:text=The%20Gaudiya%20Sampradaya%20worships%20Sri,)%20mood%2C%20in%20sakhi%20bhava.&text=Other%20Vaisnavas%20are%20also%20worshiping,following%20Radhika%27s%20great%20separation%20mood