I have not studied Sanskrit, but given my interest in Buddhism it'll be on the radar at some point. Is the Sanskrit of Indian Buddhist texts (aka "Buddhist Hybrid Sanskrit") much different from the Sanskrit of the Vedas or other ancient Hindu texts? Easier or harder?"
Acārya Śāntarakṣita was an esteemed professor at Nalanda University, as also a minor prince from a small kingdom in what is now Bengal. His sister had married Padmasambhava ̧another professor at Nalanda, and a rather notorious character. The king of Tibet had a request of Śāntarakṣita, that he might introduce Buddhism into Tibet. At first attempt this was roundly defeated by the local shamans, called Bonpo, and Śantarakṣita retreated to Nepal for safety. A second plan ensued to send Padmasambhava to Tibet for the establishment of Buddhism on more esoteric foundations. With this being successful, Śantarakṣita returned, and Buddhism was established in Tibet. A variation called Vajrayana Mahayana Buddhism was introduced. The full teachings of Nalanda and other universities, in Sanskrit, were translated into Tibetan, and indeed are mostly the only sample of these texts to now exist, excluding a collection in nepalese Nevari Sanskrit. This monumental event took place in the year 748 and onward for a few generations. This is all terribly simplified, but the key point is to introduce a sample of Buddhist Sanskrit.
So, here is first a sample of a text from Śantarakṣita, transposed into Roman script, but keeping the full use of Brahmi, which serves no useful purpose but to make life difficult for the reader.
etasmin vajramahāyāne ye kecid anupacitakuśalavāsanāsantānāḥ,samāropita bhāvabhāvanāḥ,svavikalpānilapreyamāṇamatayaḥ,sakalakalikālakalaṅkapaṅkapaṭala malīmasamānasāḥ,asamadhigata saṁsārasāgarataraṇopāyāḥ,svavikalpānalpasaṅkalpitadhiyaḥ,viṣamagranthisthānadainyapat itāḥ,durbodhagrahāveśavaśākulitacetaso'nupāsitācāryāḥ,paramārthabhāvanopadeśarahitāḥ,ś rīmanmahāsukhavajrasattvatvam,analpakalpāsaṁkhyenāpi mārgāntareṇādhigamyaṁ vajrayānopāyayuktānām ihaiva janmani anāyāsasādhyasthirasarvabhāva [svabhāvam],anādinidha[na]m,anālayam,akhilasattvasantānaṁ,svasaṁvedyasvabhāvam,ma hāpuṇyahetum,adhigamalakṣaṇaṁ,tadupāyabhū(taṁ)ca mahāvajrayānaṁ samastayānottamamāgamaṁ lakṣaṇaṁ na pratipadyante,teṣām ajñānatimirapaṭalavinivṛttaye yuktyāgamābhyām abhidhīyate kiñcit ||
And again with full sandhi, but some seperation for clarity. Compound words marked but seperated, and consonants not clustered together, as happens in various Indic scripts.
etasmin vajra.mahāyāne ye kecid anupacita.kuśala.vāsanā.santānāḥ, samāropita bhāva.bhāvanāḥ,svavikalpā.nila.preya.māṇa-matayaḥ,sakala-kalikāla.kalaṅka.paṅka.paṭala-malīmasa-mānasāḥ,asamadhigata-saṁsāra.sāgara.taraṇa.upāyāḥ,svavikalpān alpa.saṅkalpita.dhiyaḥ,viṣama.granthi.sthā.nadainya patitāḥ,durbodha.grahā.veśa.vaśā.kulita cetasas anupāsitācāryāḥ, paramārtha.bhāvana upadeśarahitāḥ, śrīman.mahāsukha.vajrasattva tvam, analpa.kalpā.saṁkhyena api mārga.antareṇa adhigamyaṁ vajrayāna.upāya.yuktānām iha eva janmani anāyāsa.sādhya.sthira-sarva.bhāva [svabhāvam], anādi.nidha[na]m, anālayam, akhila.sattva.santānaṁ, svasaṁvedya.svabhāvam, mahāpuṇyahetum, adhigama.lakṣaṇaṁ, tad upāyabhū(taṁ) ca mahāvajrayānaṁ samastaya.anuttamam āgamaṁ lakṣaṇaṁ na pratipadyante, teṣām ajñā.nati.mira.paṭala.vini.vṛttaye yuktya āgamābhyām abhidhīyate kiñcit ||
If we want to have full clarity, but take a larger amount of space, which is an irrelevant concept in the digital format, we have:
etasmin vajramahāyāne ye kecit anupacita kuśala·vāsanā·santānās,
svavikalpāt alpa·saṅkalpita dhiyas,
viṣama·granthi·sthā nadainya patitās,
durbodha·grahā·veśa·vaśā·kulita·cetasas anupāsita acāryās,
śrīmat mahāsukha vajrasattva tvam,
analpa·kalpā·saṁkhyena api mārga͡ antareṇa adhigamyam vajrayāna͡·upāya·yuktānām iha iva janmani anāyāsa·sādhya·sthira-sarva·bhāva [svabhāvam],
tat upāya·bhū(taṁ) ca mahā vajrayānam samastayāna͡·uttamam āgamam lakṣaṇam na pratipadyante,
teṣām ajñānatimira·paṭala·vinivṛttaye yuktyā gamābhyām abhidhīyate kiñcit ||
What we see here is over a thousand years after Panini and his grammar. Please observe the extensive use of compound words. Something Panini did not anticipate, and which eventually will choke Sanskrit into incomprehensability. Śāntarakṣita was a logician and an excellent teacher of Sanskrit. Buddhism moved out of the Prakṛt languages over some centuries at an earlier stage than we see here. The process was slow and at first very prakṛtik, but that is not to say it was a unique form of Sanskrit. Our sample here is quite mature, showing only some double consonants, which was the style of Sanskrit in the 8th century.
My hope is that this will inspire you to pursue your Buddhistic studies. Vast amounts of old texts are already translated, by the way, and you can be quite busy with those for a long time. It is said that Pali can be learned in two weeks if one knows Sanskrit already, as it simply is learning rules of transposing letters. I can not attest to this fact, but it is also claimed of prehomeric Greek and Vedic. Lets see!